LMFDB - Embedded newform 950.2.n.a.39.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.15
Character	$\chi$	$=$	950.39
Dual form			950.2.n.a.609.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-1.70705 - 0.554656i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.20234 + 0.386932i) q^{5} +(-0.554656 - 1.70705i) q^{6} -2.40506i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.179341 + 0.130299i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-1.70705 - 0.554656i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.20234 + 0.386932i) q^{5} +(-0.554656 - 1.70705i) q^{6} -2.40506i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.179341 + 0.130299i) q^{9} +(-1.60753 - 1.55429i) q^{10} +(-1.18730 + 0.862623i) q^{11} +(1.05502 - 1.45211i) q^{12} +(-1.66454 + 2.29105i) q^{13} +(1.94573 - 1.41366i) q^{14} +(3.97412 + 0.561025i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(6.37127 - 2.07015i) q^{17} +0.221678i q^{18} +(0.309017 + 0.951057i) q^{19} +(0.312565 - 2.21411i) q^{20} +(-1.33398 + 4.10556i) q^{21} +(-1.39575 - 0.453508i) q^{22} +(2.51443 + 3.46082i) q^{23} +1.79490 q^{24} +(4.70057 - 1.70431i) q^{25} -2.83189 q^{26} +(2.93118 + 4.03442i) q^{27} +(2.28735 + 0.743204i) q^{28} +(1.06829 - 3.28786i) q^{29} +(1.88205 + 3.54489i) q^{30} +(-0.0666792 - 0.205218i) q^{31} -1.00000i q^{32} +(2.50524 - 0.814003i) q^{33} +(5.41973 + 3.93766i) q^{34} +(0.930593 + 5.29674i) q^{35} +(-0.179341 + 0.130299i) q^{36} +(-0.317607 + 0.437149i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(4.11221 - 2.98770i) q^{39} +(1.97498 - 1.04855i) q^{40} +(3.14568 + 2.28547i) q^{41} +(-4.10556 + 1.33398i) q^{42} +3.22999i q^{43} +(-0.453508 - 1.39575i) q^{44} +(-0.445386 - 0.217569i) q^{45} +(-1.32192 + 4.06844i) q^{46} +(5.43123 + 1.76471i) q^{47} +(1.05502 + 1.45211i) q^{48} +1.21570 q^{49} +(4.14174 + 2.80107i) q^{50} -12.0243 q^{51} +(-1.66454 - 2.29105i) q^{52} +(7.14006 + 2.31995i) q^{53} +(-1.54101 + 4.74275i) q^{54} +(2.28106 - 2.35919i) q^{55} +(0.743204 + 2.28735i) q^{56} -1.79490i q^{57} +(3.28786 - 1.06829i) q^{58} +(-7.41242 - 5.38544i) q^{59} +(-1.76164 + 3.60625i) q^{60} +(0.660254 - 0.479703i) q^{61} +(0.126831 - 0.174568i) q^{62} +(0.313376 - 0.431326i) q^{63} +(0.809017 - 0.587785i) q^{64} +(2.77941 - 5.68972i) q^{65} +(2.13109 + 1.54833i) q^{66} +(-4.13267 + 1.34278i) q^{67} +6.69915i q^{68} +(-2.37271 - 7.30246i) q^{69} +(-3.73817 + 3.86621i) q^{70} +(-1.41229 + 4.34658i) q^{71} +(-0.210828 - 0.0685022i) q^{72} +(8.70445 + 11.9806i) q^{73} -0.540345 q^{74} +(-8.96943 + 0.302148i) q^{75} -1.00000 q^{76} +(2.07466 + 2.85552i) q^{77} +(4.83419 + 1.57072i) q^{78} +(-1.19856 + 3.68878i) q^{79} +(2.00916 + 0.981466i) q^{80} +(-2.97147 - 9.14526i) q^{81} +3.88827i q^{82} +(5.70810 - 1.85467i) q^{83} +(-3.49240 - 2.53738i) q^{84} +(-13.2307 + 7.02442i) q^{85} +(-2.61312 + 1.89854i) q^{86} +(-3.64726 + 5.02002i) q^{87} +(0.862623 - 1.18730i) q^{88} +(14.8234 - 10.7698i) q^{89} +(-0.0857741 - 0.488209i) q^{90} +(5.51010 + 4.00332i) q^{91} +(-4.06844 + 1.32192i) q^{92} +0.387302i q^{93} +(1.76471 + 5.43123i) q^{94} +(-1.04855 - 1.97498i) q^{95} +(-0.554656 + 1.70705i) q^{96} +(0.833092 + 0.270688i) q^{97} +(0.714570 + 0.983521i) q^{98} -0.325331 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−1.70705	−	0.554656i	−0.985568	−	0.320231i	−0.228484	−	0.973548i	$-0.573377\pi$
$3$	−1.70705	−	0.554656i	−0.985568	−	0.320231i	−0.757084	+	0.653317i	$0.773377\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−2.20234	+	0.386932i	−0.984915	+	0.173041i
$5$	−2.20234	+	0.386932i	−0.984915	+	0.173041i
$6$	−0.554656	−	1.70705i	−0.226437	−	0.696902i
$7$		−	2.40506i		−	0.909026i	−0.890740	−	0.454513i	$-0.849813\pi$
$7$		−	2.40506i		−	0.909026i	0.890740	−	0.454513i	$-0.150187\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	0.179341	+	0.130299i	0.0597804	+	0.0434330i
$10$	−1.60753	−	1.55429i	−0.508347	−	0.491511i
$11$	−1.18730	+	0.862623i	−0.357984	+	0.260091i	−0.752211	−	0.658923i	$-0.771013\pi$
$11$	−1.18730	+	0.862623i	−0.357984	+	0.260091i	0.394227	+	0.919013i	$0.371013\pi$
$12$	1.05502	−	1.45211i	0.304557	−	0.419187i
$13$	−1.66454	+	2.29105i	−0.461662	+	0.635423i	−0.974852	−	0.222852i	$-0.928463\pi$
$13$	−1.66454	+	2.29105i	−0.461662	+	0.635423i	0.513191	+	0.858275i	$0.328463\pi$
$14$	1.94573	−	1.41366i	0.520019	−	0.377816i
$15$	3.97412	+	0.561025i	1.02611	+	0.144856i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	6.37127	−	2.07015i	1.54526	−	0.502086i	0.592439	−	0.805616i	$-0.298165\pi$
$17$	6.37127	−	2.07015i	1.54526	−	0.502086i	0.952822	+	0.303530i	$0.0981653\pi$
$18$			0.221678i			0.0522500i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	0.312565	−	2.21411i	0.0698918	−	0.495091i
$21$	−1.33398	+	4.10556i	−0.291098	+	0.895907i
$22$	−1.39575	−	0.453508i	−0.297576	−	0.0966882i
$23$	2.51443	+	3.46082i	0.524296	+	0.721631i	0.986248	−	0.165274i	$-0.0528507\pi$
$23$	2.51443	+	3.46082i	0.524296	+	0.721631i	−0.461952	+	0.886905i	$0.652851\pi$
$24$	1.79490			0.366383
$25$	4.70057	−	1.70431i	0.940114	−	0.340861i
$26$	−2.83189			−0.555380
$27$	2.93118	+	4.03442i	0.564106	+	0.776425i
$28$	2.28735	+	0.743204i	0.432268	+	0.140452i
$29$	1.06829	−	3.28786i	0.198376	−	0.610539i	−0.801544	−	0.597935i	$-0.795988\pi$
$29$	1.06829	−	3.28786i	0.198376	−	0.610539i	0.999921	−	0.0126040i	$-0.00401209\pi$
$30$	1.88205	+	3.54489i	0.343614	+	0.647206i
$31$	−0.0666792	−	0.205218i	−0.0119759	−	0.0368582i	0.944890	−	0.327388i	$-0.106168\pi$
$31$	−0.0666792	−	0.205218i	−0.0119759	−	0.0368582i	−0.956866	+	0.290530i	$0.906168\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.50524	−	0.814003i	0.436107	−	0.141700i
$34$	5.41973	+	3.93766i	0.929476	+	0.675304i
$35$	0.930593	+	5.29674i	0.157299	+	0.895313i
$36$	−0.179341	+	0.130299i	−0.0298902	+	0.0217165i
$37$	−0.317607	+	0.437149i	−0.0522143	+	0.0718668i	−0.834326	−	0.551272i	$-0.814143\pi$
$37$	−0.317607	+	0.437149i	−0.0522143	+	0.0718668i	0.782111	+	0.623139i	$0.214143\pi$
$38$	−0.587785	+	0.809017i	−0.0953514	+	0.131240i
$39$	4.11221	−	2.98770i	0.658481	−	0.478414i
$40$	1.97498	−	1.04855i	0.312271	−	0.165791i
$41$	3.14568	+	2.28547i	0.491272	+	0.356930i	0.805673	−	0.592360i	$-0.201804\pi$
$41$	3.14568	+	2.28547i	0.491272	+	0.356930i	−0.314401	+	0.949290i	$0.601804\pi$
$42$	−4.10556	+	1.33398i	−0.633502	+	0.205837i
$43$			3.22999i			0.492569i	0.969198	+	0.246285i	$0.0792098\pi$
$43$			3.22999i			0.492569i	−0.969198	+	0.246285i	$0.920790\pi$
$44$	−0.453508	−	1.39575i	−0.0683689	−	0.210418i
$45$	−0.445386	−	0.217569i	−0.0663943	−	0.0324333i
$46$	−1.32192	+	4.06844i	−0.194906	+	0.599859i
$47$	5.43123	+	1.76471i	0.792226	+	0.257410i	0.677052	−	0.735936i	$-0.263257\pi$
$47$	5.43123	+	1.76471i	0.792226	+	0.257410i	0.115174	+	0.993345i	$0.463257\pi$
$48$	1.05502	+	1.45211i	0.152279	+	0.209594i
$49$	1.21570			0.173671
$50$	4.14174	+	2.80107i	0.585730	+	0.396132i
$51$	−12.0243			−1.68374
$52$	−1.66454	−	2.29105i	−0.230831	−	0.317711i
$53$	7.14006	+	2.31995i	0.980763	+	0.318669i	0.755153	−	0.655549i	$-0.227563\pi$
$53$	7.14006	+	2.31995i	0.980763	+	0.318669i	0.225610	+	0.974218i	$0.427563\pi$
$54$	−1.54101	+	4.74275i	−0.209705	+	0.645406i
$55$	2.28106	−	2.35919i	0.307578	−	0.318113i
$56$	0.743204	+	2.28735i	0.0993148	+	0.305659i
$57$		−	1.79490i		−	0.237741i
$58$	3.28786	−	1.06829i	0.431717	−	0.140273i
$59$	−7.41242	−	5.38544i	−0.965015	−	0.701125i	−0.0107051	−	0.999943i	$-0.503408\pi$
$59$	−7.41242	−	5.38544i	−0.965015	−	0.701125i	−0.954310	+	0.298818i	$0.903408\pi$
$60$	−1.76164	+	3.60625i	−0.227426	+	0.465565i
$61$	0.660254	−	0.479703i	0.0845369	−	0.0614196i	−0.544714	−	0.838622i	$-0.683362\pi$
$61$	0.660254	−	0.479703i	0.0845369	−	0.0614196i	0.629251	+	0.777202i	$0.283362\pi$
$62$	0.126831	−	0.174568i	0.0161076	−	0.0221702i
$63$	0.313376	−	0.431326i	0.0394817	−	0.0543419i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	2.77941	−	5.68972i	0.344743	−	0.705723i
$66$	2.13109	+	1.54833i	0.262319	+	0.190586i
$67$	−4.13267	+	1.34278i	−0.504886	+	0.164047i	−0.550375	−	0.834918i	$-0.685515\pi$
$67$	−4.13267	+	1.34278i	−0.504886	+	0.164047i	0.0454894	+	0.998965i	$0.485515\pi$
$68$			6.69915i			0.812391i
$69$	−2.37271	−	7.30246i	−0.285641	−	0.879113i
$70$	−3.73817	+	3.86621i	−0.446796	+	0.462101i
$71$	−1.41229	+	4.34658i	−0.167608	+	0.515844i	−0.999219	−	0.0395143i	$-0.987419\pi$
$71$	−1.41229	+	4.34658i	−0.167608	+	0.515844i	0.831611	+	0.555358i	$0.187419\pi$
$72$	−0.210828	−	0.0685022i	−0.0248463	−	0.00807306i
$73$	8.70445	+	11.9806i	1.01878	+	1.40223i	0.913057	+	0.407832i	$0.133715\pi$
$73$	8.70445	+	11.9806i	1.01878	+	1.40223i	0.105721	+	0.994396i	$0.466285\pi$
$74$	−0.540345			−0.0628139
$75$	−8.96943	+	0.302148i	−1.03570	+	0.0348890i
$76$	−1.00000			−0.114708
$77$	2.07466	+	2.85552i	0.236429	+	0.325417i
$78$	4.83419	+	1.57072i	0.547365	+	0.177850i
$79$	−1.19856	+	3.68878i	−0.134848	+	0.415021i	−0.995566	−	0.0940614i	$-0.970015\pi$
$79$	−1.19856	+	3.68878i	−0.134848	+	0.415021i	0.860718	+	0.509082i	$0.170015\pi$
$80$	2.00916	+	0.981466i	0.224631	+	0.109731i
$81$	−2.97147	−	9.14526i	−0.330164	−	1.01614i
$82$			3.88827i			0.429388i
$83$	5.70810	−	1.85467i	0.626545	−	0.203577i	0.0215012	−	0.999769i	$-0.493155\pi$
$83$	5.70810	−	1.85467i	0.626545	−	0.203577i	0.605044	+	0.796192i	$0.293155\pi$
$84$	−3.49240	−	2.53738i	−0.381052	−	0.276851i
$85$	−13.2307	+	7.02442i	−1.43507	+	0.761905i
$86$	−2.61312	+	1.89854i	−0.281780	+	0.204725i
$87$	−3.64726	+	5.02002i	−0.391027	+	0.538202i
$88$	0.862623	−	1.18730i	0.0919560	−	0.126567i
$89$	14.8234	−	10.7698i	1.57127	−	1.14160i	0.645347	−	0.763889i	$-0.276713\pi$
$89$	14.8234	−	10.7698i	1.57127	−	1.14160i	0.925925	−	0.377707i	$-0.123287\pi$
$90$	−0.0857741	−	0.488209i	−0.00904139	−	0.0514618i
$91$	5.51010	+	4.00332i	0.577616	+	0.419662i
$92$	−4.06844	+	1.32192i	−0.424164	+	0.137819i
$93$			0.387302i			0.0401613i
$94$	1.76471	+	5.43123i	0.182016	+	0.560188i
$95$	−1.04855	−	1.97498i	−0.107579	−	0.202628i
$96$	−0.554656	+	1.70705i	−0.0566093	+	0.174226i
$97$	0.833092	+	0.270688i	0.0845877	+	0.0274842i	0.351005	−	0.936374i	$-0.385840\pi$
$97$	0.833092	+	0.270688i	0.0845877	+	0.0274842i	−0.266417	+	0.963858i	$0.585840\pi$
$98$	0.714570	+	0.983521i	0.0721825	+	0.0993507i
$99$	−0.325331			−0.0326969
$100$	0.168337	+	4.99717i	0.0168337	+	0.499717i
$101$	3.81763			0.379868			0.189934	−	0.981797i	$-0.439173\pi$
$101$	3.81763			0.379868			0.189934	+	0.981797i	$0.439173\pi$
$102$	−7.06772	−	9.72789i	−0.699809	−	0.963204i
$103$	−0.215337	−	0.0699673i	−0.0212178	−	0.00689408i	0.298389	−	0.954444i	$-0.403551\pi$
$103$	−0.215337	−	0.0699673i	−0.0212178	−	0.00689408i	−0.319607	+	0.947550i	$0.603551\pi$
$104$	0.875103	−	2.69329i	0.0858109	−	0.264099i
$105$	1.34930	−	9.55799i	0.131678	−	0.932764i
$106$	2.31995	+	7.14006i	0.225333	+	0.693504i
$107$		−	6.88505i		−	0.665603i	−0.942997	−	0.332802i	$-0.892006\pi$
$107$		−	6.88505i		−	0.665603i	0.942997	−	0.332802i	$-0.107994\pi$
$108$	−4.74275	+	1.54101i	−0.456371	+	0.148284i
$109$	−6.16922	−	4.48220i	−0.590904	−	0.429317i	0.251735	−	0.967796i	$-0.418999\pi$
$109$	−6.16922	−	4.48220i	−0.590904	−	0.429317i	−0.842639	+	0.538479i	$0.818999\pi$
$110$	3.24940	+	0.458716i	0.309818	+	0.0437368i
$111$	0.784640	−	0.570074i	0.0744747	−	0.0541090i
$112$	−1.41366	+	1.94573i	−0.133578	+	0.183854i
$113$	−2.01595	+	2.77472i	−0.189645	+	0.261024i	−0.893243	−	0.449575i	$-0.851576\pi$
$113$	−2.01595	+	2.77472i	−0.189645	+	0.261024i	0.703598	+	0.710598i	$0.251576\pi$
$114$	1.45211	−	1.05502i	0.136002	−	0.0988115i
$115$	−6.87673	−	6.64898i	−0.641259	−	0.620021i
$116$	2.79682	+	2.03201i	0.259678	+	0.188667i
$117$	−0.597042	+	0.193991i	−0.0551966	+	0.0179345i
$118$		−	9.16226i		−	0.843454i
$119$	−4.97883	−	15.3233i	−0.456409	−	1.40468i
$120$	−3.95298	+	0.694505i	−0.360856	+	0.0633993i
$121$	−2.73363	+	8.41324i	−0.248511	+	0.764840i
$122$	0.776175	+	0.252195i	0.0702716	+	0.0228326i
$123$	−4.10220	−	5.64619i	−0.369882	−	0.509100i
$124$	0.215779			0.0193775
$125$	−9.69278	+	5.57225i	−0.866949	+	0.498398i
$126$	0.533148			0.0474966
$127$	0.316418	+	0.435512i	0.0280775	+	0.0386454i	0.822825	−	0.568295i	$-0.192397\pi$
$127$	0.316418	+	0.435512i	0.0280775	+	0.0386454i	−0.794747	+	0.606940i	$0.792397\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	1.79153	−	5.51377i	0.157736	−	0.485461i
$130$	6.23678	−	1.09575i	0.547002	−	0.0961035i
$131$	−3.89439	−	11.9857i	−0.340254	−	1.04719i	−0.964076	−	0.265628i	$-0.914421\pi$
$131$	−3.89439	−	11.9857i	−0.340254	−	1.04719i	0.623822	−	0.781567i	$-0.285579\pi$
$132$			2.63417i			0.229275i
$133$	2.28735	−	0.743204i	0.198338	−	0.0644439i
$134$	−3.51546	−	2.55413i	−0.303689	−	0.220643i
$135$	−8.01649	−	7.75099i	−0.689949	−	0.667099i
$136$	−5.41973	+	3.93766i	−0.464738	+	0.337652i
$137$	12.3145	−	16.9494i	1.05210	−	1.44809i	0.165121	−	0.986273i	$-0.447198\pi$
$137$	12.3145	−	16.9494i	1.05210	−	1.44809i	0.886976	−	0.461815i	$-0.152802\pi$
$138$	4.51317	−	6.21184i	0.384186	−	0.528787i
$139$	18.2379	−	13.2506i	1.54692	−	1.12390i	0.601116	−	0.799162i	$-0.294723\pi$
$139$	18.2379	−	13.2506i	1.54692	−	1.12390i	0.945803	−	0.324741i	$-0.105277\pi$
$140$	−5.32507	−	0.751738i	−0.450051	−	0.0635334i
$141$	−8.29259	−	6.02492i	−0.698362	−	0.507390i
$142$	−4.34658	+	1.41229i	−0.364757	+	0.118517i
$143$		−	4.15604i		−	0.347545i
$144$	−0.0685022	−	0.210828i	−0.00570852	−	0.0175690i
$145$	−1.08056	+	7.65432i	−0.0897353	+	0.635656i
$146$	−4.57620	+	14.0841i	−0.378729	+	1.16561i
$147$	−2.07526	−	0.674294i	−0.171165	−	0.0556149i
$148$	−0.317607	−	0.437149i	−0.0261071	−	0.0359334i
$149$	−7.47667			−0.612513			−0.306256	−	0.951949i	$-0.599077\pi$
$149$	−7.47667			−0.612513			−0.306256	+	0.951949i	$0.599077\pi$
$150$	−5.51654	−	7.07882i	−0.450424	−	0.577983i
$151$	−0.406951			−0.0331172			−0.0165586	−	0.999863i	$-0.505271\pi$
$151$	−0.406951			−0.0331172			−0.0165586	+	0.999863i	$0.505271\pi$
$152$	−0.587785	−	0.809017i	−0.0476757	−	0.0656199i
$153$	1.41237	+	0.458907i	0.114183	+	0.0371004i
$154$	−1.09071	+	3.35687i	−0.0878921	+	0.270504i
$155$	0.226255	+	0.426158i	0.0181733	+	0.0342298i
$156$	1.57072	+	4.83419i	0.125759	+	0.387045i
$157$			3.99551i			0.318876i	0.987208	+	0.159438i	$0.0509682\pi$
$157$			3.99551i			0.318876i	−0.987208	+	0.159438i	$0.949032\pi$
$158$	−3.68878	+	1.19856i	−0.293464	+	0.0953522i
$159$	−10.9017	−	7.92055i	−0.864561	−	0.628140i
$160$	0.386932	+	2.20234i	0.0305896	+	0.174110i
$161$	8.32348	−	6.04736i	0.655982	−	0.476599i
$162$	5.65208	−	7.77942i	0.444069	−	0.611209i
$163$	−12.6033	+	17.3469i	−0.987164	+	1.35872i	−0.0542854	+	0.998525i	$0.517288\pi$
$163$	−12.6033	+	17.3469i	−0.987164	+	1.35872i	−0.932879	+	0.360190i	$0.882712\pi$
$164$	−3.14568	+	2.28547i	−0.245636	+	0.178465i
$165$	−5.20242	+	2.76207i	−0.405008	+	0.215027i
$166$	4.85560	+	3.52780i	0.376868	+	0.273810i
$167$	2.75834	−	0.896239i	0.213447	−	0.0693531i	−0.200342	−	0.979726i	$-0.564205\pi$
$167$	2.75834	−	0.896239i	0.213447	−	0.0693531i	0.413789	+	0.910373i	$0.364205\pi$
$168$		−	4.31685i		−	0.333052i
$169$	1.53902	+	4.73663i	0.118387	+	0.364356i
$170$	−13.4597	−	6.57499i	−1.03231	−	0.504279i
$171$	−0.0685022	+	0.210828i	−0.00523850	+	0.0161224i
$172$	−3.07190	−	0.998122i	−0.234231	−	0.0761061i
$173$	6.76605	+	9.31267i	0.514413	+	0.708029i	0.984656	−	0.174508i	$-0.0558336\pi$
$173$	6.76605	+	9.31267i	0.514413	+	0.708029i	−0.470243	+	0.882537i	$0.655834\pi$
$174$	−6.20508			−0.470406
$175$	−4.09896	−	11.3051i	−0.309852	−	0.854588i
$176$	1.46758			0.110623
$177$	9.66634	+	13.3046i	0.726567	+	1.00003i
$178$	17.4259	+	5.66202i	1.30613	+	0.424386i
$179$	2.53556	−	7.80365i	0.189517	−	0.583272i	−0.810480	−	0.585766i	$-0.800794\pi$
$179$	2.53556	−	7.80365i	0.189517	−	0.583272i	0.999997	+	0.00249391i	$0.000793837\pi$
$180$	0.344553	−	0.356355i	0.0256814	−	0.0265611i
$181$	−0.401463	−	1.23557i	−0.0298405	−	0.0918396i	0.935027	−	0.354576i	$-0.115375\pi$
$181$	−0.401463	−	1.23557i	−0.0298405	−	0.0918396i	−0.964868	+	0.262737i	$0.915375\pi$
$182$			6.81086i			0.504855i
$183$	−1.39316	+	0.452665i	−0.102985	+	0.0334620i
$184$	−3.46082	−	2.51443i	−0.255135	−	0.185367i
$185$	0.530331	−	1.08564i	0.0389907	−	0.0798179i
$186$	−0.313334	+	0.227650i	−0.0229747	+	0.0166921i
$187$	−5.77885	+	7.95390i	−0.422591	+	0.581647i
$188$	−3.35668	+	4.62008i	−0.244811	+	0.336954i
$189$	9.70302	−	7.04965i	0.705791	−	0.512787i
$190$	0.981466	−	2.00916i	0.0712031	−	0.145760i
$191$	−7.57145	−	5.50098i	−0.547851	−	0.398037i	0.279142	−	0.960250i	$-0.409950\pi$
$191$	−7.57145	−	5.50098i	−0.547851	−	0.398037i	−0.826992	+	0.562213i	$0.809950\pi$
$192$	−1.70705	+	0.554656i	−0.123196	+	0.0400288i
$193$			1.75533i			0.126352i	0.998002	+	0.0631758i	$0.0201229\pi$
$193$			1.75533i			0.126352i	−0.998002	+	0.0631758i	$0.979877\pi$
$194$	0.270688	+	0.833092i	0.0194343	+	0.0598125i
$195$	−7.90044	+	8.17105i	−0.565762	+	0.585141i
$196$	−0.375672	+	1.15620i	−0.0268337	+	0.0825856i
$197$	5.36013	+	1.74161i	0.381894	+	0.124085i	0.493672	−	0.869648i	$-0.335655\pi$
$197$	5.36013	+	1.74161i	0.381894	+	0.124085i	−0.111778	+	0.993733i	$0.535655\pi$
$198$	−0.191224	−	0.263198i	−0.0135897	−	0.0187047i
$199$	5.36459			0.380286			0.190143	−	0.981756i	$-0.439105\pi$
$199$	5.36459			0.380286			0.190143	+	0.981756i	$0.439105\pi$
$200$	−3.94385	+	3.07345i	−0.278872	+	0.217326i
$201$	7.79947			0.550132
$202$	2.24395	+	3.08853i	0.157883	+	0.217308i
$203$	−7.90748	−	2.56930i	−0.554996	−	0.180329i
$204$	3.71572	−	11.4358i	0.260153	−	0.800667i
$205$	−7.81216	−	3.81621i	−0.545625	−	0.266536i
$206$	−0.0699673	−	0.215337i	−0.00487485	−	0.0150033i
$207$			0.948296i			0.0659111i
$208$	2.69329	−	0.875103i	0.186746	−	0.0606775i
$209$	−1.18730	−	0.862623i	−0.0821272	−	0.0596689i
$210$	8.52567	−	4.52644i	0.588327	−	0.312354i
$211$	−13.6897	+	9.94614i	−0.942437	+	0.684720i	−0.949006	−	0.315258i	$-0.897909\pi$
$211$	−13.6897	+	9.94614i	−0.942437	+	0.684720i	0.00656923	+	0.999978i	$0.497909\pi$
$212$	−4.41280	+	6.07370i	−0.303072	+	0.417143i
$213$	4.82171	−	6.63651i	0.330378	−	0.454727i
$214$	5.57013	−	4.04693i	0.380766	−	0.276643i
$215$	−1.24979	−	7.11353i	−0.0852347	−	0.485138i
$216$	−4.03442	−	2.93118i	−0.274508	−	0.199441i
$217$	−0.493560	+	0.160367i	−0.0335050	+	0.0108864i
$218$		−	7.62557i		−	0.516469i
$219$	−8.21383	−	25.2796i	−0.555039	−	1.70824i
$220$	1.53884	+	2.89844i	0.103748	+	0.195413i
$221$	−5.86245	+	18.0428i	−0.394351	+	1.21369i
$222$	0.922399	+	0.299706i	0.0619074	+	0.0201149i
$223$	−2.99112	−	4.11692i	−0.200300	−	0.275689i	0.697037	−	0.717035i	$-0.254501\pi$
$223$	−2.99112	−	4.11692i	−0.200300	−	0.275689i	−0.897337	+	0.441346i	$0.854501\pi$
$224$	−2.40506			−0.160695
$225$	1.06507	+	0.306827i	0.0710050	+	0.0204551i
$226$	−3.42974			−0.228143
$227$	9.34890	+	12.8677i	0.620508	+	0.854056i	0.997390	−	0.0722052i	$-0.0230036\pi$
$227$	9.34890	+	12.8677i	0.620508	+	0.854056i	−0.376882	+	0.926261i	$0.623004\pi$
$228$	1.70705	+	0.554656i	0.113052	+	0.0367330i
$229$	−3.92604	+	12.0831i	−0.259440	+	0.798475i	0.733482	+	0.679709i	$0.237894\pi$
$229$	−3.92604	+	12.0831i	−0.259440	+	0.798475i	−0.992922	+	0.118766i	$0.962106\pi$
$230$	1.33710	−	9.47157i	0.0881655	−	0.624537i
$231$	−1.95772	−	6.02525i	−0.128809	−	0.396433i
$232$			3.45706i			0.226967i
$233$	3.39201	−	1.10213i	0.222218	−	0.0722029i	−0.195792	−	0.980645i	$-0.562728\pi$
$233$	3.39201	−	1.10213i	0.222218	−	0.0722029i	0.418010	+	0.908443i	$0.362728\pi$
$234$	−0.507875	−	0.368993i	−0.0332008	−	0.0241218i
$235$	−12.6442	−	1.78498i	−0.824817	−	0.116439i
$236$	7.41242	−	5.38544i	0.482508	−	0.350562i
$237$	4.09201	−	5.63217i	0.265805	−	0.365849i
$238$	9.47030	−	13.0348i	0.613869	−	0.844918i
$239$	−12.5539	+	9.12094i	−0.812045	+	0.589985i	−0.914423	−	0.404761i	$-0.867355\pi$
$239$	−12.5539	+	9.12094i	−0.812045	+	0.589985i	0.102378	+	0.994746i	$0.467355\pi$
$240$	−2.88537	−	2.78981i	−0.186250	−	0.180081i
$241$	−6.23711	−	4.53153i	−0.401768	−	0.291901i	0.368493	−	0.929631i	$-0.379874\pi$
$241$	−6.23711	−	4.53153i	−0.401768	−	0.291901i	−0.770261	+	0.637729i	$0.779874\pi$
$242$	−8.41324	+	2.73363i	−0.540823	+	0.175724i
$243$			2.29914i			0.147490i
$244$	0.252195	+	0.776175i	0.0161451	+	0.0496895i
$245$	−2.67738	+	0.470392i	−0.171051	+	0.0300523i
$246$	2.15665	−	6.63749i	0.137503	−	0.423191i
$247$	−2.69329	−	0.875103i	−0.171370	−	0.0556815i
$248$	0.126831	+	0.174568i	0.00805380	+	0.0110851i
$249$	−10.7727			−0.682695
$250$	−10.2053	−	4.56634i	−0.645441	−	0.288800i
$251$	6.46535			0.408089			0.204045	−	0.978962i	$-0.434591\pi$
$251$	6.46535			0.408089			0.204045	+	0.978962i	$0.434591\pi$
$252$	0.313376	+	0.431326i	0.0197409	+	0.0271710i
$253$	−5.97077	−	1.94002i	−0.375379	−	0.121968i
$254$	−0.166351	+	0.511975i	−0.0104378	+	0.0321242i
$255$	26.4816	−	4.65259i	1.65834	−	0.291357i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			2.29300i			0.143033i	0.997439	+	0.0715167i	$0.0227839\pi$
$257$			2.29300i			0.143033i	−0.997439	+	0.0715167i	$0.977216\pi$
$258$	5.51377	−	1.79153i	0.343272	−	0.111536i
$259$	1.05137	+	0.763863i	0.0653288	+	0.0474642i
$260$	4.55236	+	4.40159i	0.282326	+	0.272975i
$261$	0.619992	−	0.450451i	0.0383766	−	0.0278822i
$262$	7.40756	−	10.1956i	0.457641	−	0.629888i
$263$	−14.9647	+	20.5972i	−0.922765	+	1.27008i	0.0398510	+	0.999206i	$0.487312\pi$
$263$	−14.9647	+	20.5972i	−0.922765	+	1.27008i	−0.962616	+	0.270871i	$0.912688\pi$
$264$	−2.13109	+	1.54833i	−0.131159	+	0.0952929i
$265$	−16.6225	−	2.34659i	−1.02111	−	0.144150i
$266$	1.94573	+	1.41366i	0.119300	+	0.0866769i
$267$	−31.2778	+	10.1628i	−1.91417	+	0.621952i
$268$		−	4.34534i		−	0.265434i
$269$	8.31027	+	25.5764i	0.506686	+	1.55942i	0.797918	+	0.602766i	$0.205935\pi$
$269$	8.31027	+	25.5764i	0.506686	+	1.55942i	−0.291232	+	0.956653i	$0.594065\pi$
$270$	1.55871	−	11.0414i	0.0948599	−	0.671958i
$271$	8.51503	−	26.2066i	0.517251	−	1.59194i	−0.261897	−	0.965096i	$-0.584348\pi$
$271$	8.51503	−	26.2066i	0.517251	−	1.59194i	0.779148	−	0.626840i	$-0.215652\pi$
$272$	−6.37127	−	2.07015i	−0.386315	−	0.125521i
$273$	−7.18558	−	9.89010i	−0.434891	−	0.598576i
$274$	20.9507			1.26568
$275$	−4.11081	+	6.07834i	−0.247891	+	0.366538i
$276$	7.67826			0.462177
$277$	16.2511	+	22.3677i	0.976433	+	1.34394i	0.938729	+	0.344655i	$0.112004\pi$
$277$	16.2511	+	22.3677i	0.976433	+	1.34394i	0.0377035	+	0.999289i	$0.487996\pi$
$278$	21.4399	+	6.96626i	1.28588	+	0.417809i
$279$	0.0147813	−	0.0454922i	0.000884934	−	0.00272355i
$280$	−2.52183	−	4.74993i	−0.150708	−	0.283863i
$281$	8.90055	+	27.3931i	0.530962	+	1.63413i	0.752215	+	0.658918i	$0.228986\pi$
$281$	8.90055	+	27.3931i	0.530962	+	1.63413i	−0.221252	+	0.975217i	$0.571014\pi$
$282$		−	10.2502i		−	0.610391i
$283$	16.0675	−	5.22066i	0.955117	−	0.310336i	0.210324	−	0.977632i	$-0.432548\pi$
$283$	16.0675	−	5.22066i	0.955117	−	0.310336i	0.744793	+	0.667296i	$0.232548\pi$
$284$	−3.69742	−	2.68633i	−0.219402	−	0.159405i
$285$	0.694505	+	3.95298i	0.0411389	+	0.234154i
$286$	3.36230	−	2.44286i	0.198817	−	0.144449i
$287$	5.49668	−	7.56554i	0.324459	−	0.446579i
$288$	0.130299	−	0.179341i	0.00767794	−	0.0105678i
$289$	22.5543	−	16.3866i	1.32672	−	0.963921i
$290$	−6.82761	+	3.62491i	−0.400931	+	0.212862i
$291$	−1.27199	−	0.924158i	−0.0745656	−	0.0541751i
$292$	−14.0841	+	4.57620i	−0.824209	+	0.267802i
$293$		−	26.3137i		−	1.53727i	−0.639690	−	0.768633i	$-0.720937\pi$
$293$		−	26.3137i		−	1.53727i	0.639690	−	0.768633i	$-0.279063\pi$
$294$	−0.674294	−	2.07526i	−0.0393256	−	0.121032i
$295$	18.4084	+	8.99245i	1.07178	+	0.523561i
$296$	0.166976	−	0.513899i	0.00970528	−	0.0298698i
$297$	−6.96037	−	2.26156i	−0.403882	−	0.131229i
$298$	−4.39468	−	6.04876i	−0.254577	−	0.350395i
$299$	−12.1143			−0.700588
$300$	2.48435	−	8.62380i	0.143434	−	0.497895i
$301$	7.76831			0.447758
$302$	−0.239200	−	0.329230i	−0.0137644	−	0.0189451i
$303$	−6.51690	−	2.11747i	−0.374386	−	0.121645i
$304$	0.309017	−	0.951057i	0.0177233	−	0.0545468i
$305$	−1.26849	+	1.31194i	−0.0726335	+	0.0751214i
$306$	0.458907	+	1.41237i	0.0262340	+	0.0807398i
$307$			25.4594i			1.45305i	0.687142	+	0.726524i	$0.258865\pi$
$307$			25.4594i			1.45305i	−0.687142	+	0.726524i	$0.741135\pi$
$308$	−3.35687	+	1.09071i	−0.191275	+	0.0621491i
$309$	0.328785	+	0.238876i	0.0187039	+	0.0135892i
$310$	−0.211779	+	0.433534i	−0.0120283	+	0.0246231i
$311$	12.2379	−	8.89132i	0.693945	−	0.504180i	−0.184010	−	0.982924i	$-0.558908\pi$
$311$	12.2379	−	8.89132i	0.693945	−	0.504180i	0.877955	+	0.478744i	$0.158908\pi$
$312$	−2.98770	+	4.11221i	−0.169145	+	0.232808i
$313$	5.22315	−	7.18905i	0.295230	−	0.406349i	−0.635474	−	0.772122i	$-0.719195\pi$
$313$	5.22315	−	7.18905i	0.295230	−	0.406349i	0.930704	+	0.365773i	$0.119195\pi$
$314$	−3.23243	+	2.34850i	−0.182417	+	0.132534i
$315$	−0.523267	+	1.07118i	−0.0294827	+	0.0603541i
$316$	−3.13787	−	2.27979i	−0.176519	−	0.128248i
$317$	32.6773	−	10.6175i	1.83534	−	0.596338i	0.836511	−	0.547951i	$-0.184592\pi$
$317$	32.6773	−	10.6175i	1.83534	−	0.596338i	0.998829	−	0.0483872i	$-0.0154081\pi$
$318$		−	13.4752i		−	0.755654i
$319$	1.56780	+	4.82520i	0.0877801	+	0.270159i
$320$	−1.55429	+	1.60753i	−0.0868877	+	0.0898639i
$321$	−3.81883	+	11.7532i	−0.213147	+	0.655998i
$322$	9.78483	+	3.17929i	0.545287	+	0.177175i
$323$	3.93766	+	5.41973i	0.219097	+	0.301562i
$324$	9.61589			0.534216
$325$	−3.91965	+	13.6061i	−0.217423	+	0.754732i
$326$	−21.4420			−1.18756
$327$	8.04511	+	11.0731i	0.444896	+	0.612346i
$328$	−3.69797	−	1.20154i	−0.204186	−	0.0663441i
$329$	4.24423	−	13.0624i	0.233992	−	0.720154i
$330$	−5.29247	−	2.58535i	−0.291341	−	0.142319i
$331$	−8.69277	−	26.7536i	−0.477798	−	1.47051i	−0.842147	−	0.539248i	$-0.818709\pi$
$331$	−8.69277	−	26.7536i	−0.477798	−	1.47051i	0.364349	−	0.931262i	$-0.381291\pi$
$332$			6.00185i			0.329394i
$333$	−0.113920	+	0.0370149i	−0.00624278	+	0.00202840i
$334$	2.34638	+	1.70475i	0.128388	+	0.0932797i
$335$	8.58196	−	4.55632i	0.468882	−	0.248939i
$336$	3.49240	−	2.53738i	0.190526	−	0.138425i
$337$	2.58411	−	3.55672i	0.140765	−	0.193747i	−0.732813	−	0.680430i	$-0.761793\pi$
$337$	2.58411	−	3.55672i	0.140765	−	0.193747i	0.873579	+	0.486683i	$0.161793\pi$
$338$	−2.92740	+	4.02922i	−0.159230	+	0.219161i
$339$	4.98035	−	3.61844i	0.270496	−	0.196527i
$340$	−2.59211	−	14.7538i	−0.140577	−	0.800136i
$341$	0.256194	+	0.186136i	0.0138737	+	0.0100798i
$342$	−0.210828	+	0.0685022i	−0.0114003	+	0.00370418i
$343$		−	19.7592i		−	1.06690i
$344$	−0.998122	−	3.07190i	−0.0538151	−	0.165626i
$345$	8.05106	+	15.1644i	0.433455	+	0.816423i
$346$	−3.55712	+	10.9477i	−0.191232	+	0.588552i
$347$	3.78274	+	1.22909i	0.203068	+	0.0659808i	0.408785	−	0.912631i	$-0.365953\pi$
$347$	3.78274	+	1.22909i	0.203068	+	0.0659808i	−0.205717	+	0.978612i	$0.565953\pi$
$348$	−3.64726	−	5.02002i	−0.195513	−	0.269101i
$349$	8.98545			0.480980			0.240490	−	0.970652i	$-0.422692\pi$
$349$	8.98545			0.480980			0.240490	+	0.970652i	$0.422692\pi$
$350$	6.73674	−	9.96112i	0.360094	−	0.532444i
$351$	−14.1221			−0.753784
$352$	0.862623	+	1.18730i	0.0459780	+	0.0632833i
$353$	19.0851	+	6.20114i	1.01580	+	0.330053i	0.769162	−	0.639054i	$-0.220674\pi$
$353$	19.0851	+	6.20114i	1.01580	+	0.330053i	0.246638	+	0.969108i	$0.420674\pi$
$354$	−5.08190	+	15.6405i	−0.270100	+	0.831282i
$355$	1.42851	−	10.1191i	0.0758173	−	0.537066i
$356$	5.66202	+	17.4259i	0.300086	+	0.923571i
$357$			28.9192i			1.53057i
$358$	7.80365	−	2.53556i	0.412436	−	0.134008i
$359$	−5.03611	−	3.65895i	−0.265796	−	0.193112i	0.446903	−	0.894583i	$-0.352527\pi$
$359$	−5.03611	−	3.65895i	−0.265796	−	0.193112i	−0.712698	+	0.701471i	$0.752527\pi$
$360$	0.490820	+	0.0692888i	0.0258685	+	0.00365184i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	0.763627	−	1.05104i	0.0401354	−	0.0552416i
$363$	9.33290	−	12.8456i	0.489850	−	0.674221i
$364$	−5.51010	+	4.00332i	−0.288808	+	0.209831i
$365$	−23.8058	−	23.0174i	−1.24605	−	1.20478i
$366$	−1.18509	−	0.861020i	−0.0619458	−	0.0450062i
$367$	−7.66490	+	2.49048i	−0.400104	+	0.130002i	−0.502155	−	0.864777i	$-0.667459\pi$
$367$	−7.66490	+	2.49048i	−0.400104	+	0.130002i	0.102051	+	0.994779i	$0.467459\pi$
$368$		−	4.27781i		−	0.222996i
$369$	0.266355	+	0.819757i	0.0138659	+	0.0426748i
$370$	1.19002	−	0.209077i	0.0618663	−	0.0108694i
$371$	5.57960	−	17.1723i	0.289679	−	0.891539i
$372$	−0.368346	−	0.119683i	−0.0190978	−	0.00620526i
$373$	1.16279	+	1.60044i	0.0602067	+	0.0828674i	0.838059	−	0.545580i	$-0.183691\pi$
$373$	1.16279	+	1.60044i	0.0602067	+	0.0828674i	−0.777852	+	0.628448i	$0.783691\pi$
$374$	−9.83156			−0.508378
$375$	19.6368	−	4.13599i	1.01404	−	0.213581i
$376$	−5.71073			−0.294508
$377$	5.75442	+	7.92028i	0.296368	+	0.407915i
$378$	11.4066	+	3.70622i	0.586691	+	0.190628i
$379$	−11.5465	+	35.5366i	−0.593106	+	1.82539i	−0.0291718	+	0.999574i	$0.509287\pi$
$379$	−11.5465	+	35.5366i	−0.593106	+	1.82539i	−0.563935	+	0.825819i	$0.690713\pi$
$380$	2.20234	−	0.386932i	0.112977	−	0.0198492i
$381$	−0.298583	−	0.918945i	−0.0152969	−	0.0470790i
$382$		−	9.35882i		−	0.478839i
$383$	−10.3518	+	3.36350i	−0.528952	+	0.171867i	−0.561304	−	0.827610i	$-0.689700\pi$
$383$	−10.3518	+	3.36350i	−0.528952	+	0.171867i	0.0323522	+	0.999477i	$0.489700\pi$
$384$	−1.45211	−	1.05502i	−0.0741025	−	0.0538386i
$385$	−5.67399	−	5.48607i	−0.289173	−	0.279596i
$386$	−1.42009	+	1.03176i	−0.0722809	+	0.0525152i
$387$	−0.420865	+	0.579270i	−0.0213937	+	0.0294460i
$388$	−0.514879	+	0.708670i	−0.0261390	+	0.0359773i
$389$	27.7206	−	20.1402i	1.40549	−	1.02115i	0.411532	−	0.911395i	$-0.364994\pi$
$389$	27.7206	−	20.1402i	1.40549	−	1.02115i	0.993959	−	0.109753i	$-0.0350061\pi$
$390$	−11.2543	−	1.58876i	−0.569883	−	0.0804501i
$391$	23.1846	+	16.8446i	1.17249	+	0.851867i
$392$	−1.15620	+	0.375672i	−0.0583969	+	0.0189743i
$393$			22.6203i			1.14104i
$394$	1.74161	+	5.36013i	0.0877412	+	0.270040i
$395$	1.21232	−	8.58770i	0.0609985	−	0.432094i
$396$	0.100533	−	0.309408i	0.00505196	−	0.0155483i
$397$	22.5552	+	7.32863i	1.13201	+	0.367813i	0.814340	−	0.580387i	$-0.197099\pi$
$397$	22.5552	+	7.32863i	1.13201	+	0.367813i	0.317672	+	0.948201i	$0.397099\pi$
$398$	3.15323	+	4.34005i	0.158057	+	0.217547i
$399$	−4.31685			−0.216113
$400$	−4.80461	−	1.38411i	−0.240230	−	0.0692056i
$401$	−33.2073			−1.65829			−0.829146	−	0.559032i	$-0.811173\pi$
$401$	−33.2073			−1.65829			−0.829146	+	0.559032i	$0.811173\pi$
$402$	4.58441	+	6.30990i	0.228650	+	0.314709i
$403$	0.581154	+	0.188828i	0.0289493	+	0.00940621i
$404$	−1.17971	+	3.63078i	−0.0586929	+	0.180638i
$405$	10.0828	+	18.9912i	0.501017	+	0.943679i
$406$	−2.56930	−	7.90748i	−0.127512	−	0.392442i
$407$		−	0.793002i		−	0.0393076i
$408$	11.4358	−	3.71572i	0.566157	−	0.183956i
$409$	15.5627	+	11.3069i	0.769524	+	0.559092i	0.901817	−	0.432119i	$-0.142234\pi$
$409$	15.5627	+	11.3069i	0.769524	+	0.559092i	−0.132293	+	0.991211i	$0.542234\pi$
$410$	−1.50449	−	8.56328i	−0.0743017	−	0.422910i
$411$	−30.4226	+	22.1033i	−1.50064	+	1.09028i
$412$	0.133086	−	0.183177i	0.00655666	−	0.00902447i
$413$	−12.9523	+	17.8273i	−0.637341	+	0.877224i
$414$	−0.767188	+	0.557394i	−0.0377052	+	0.0273944i
$415$	−11.8535	+	6.29326i	−0.581867	+	0.308924i
$416$	2.29105	+	1.66454i	0.112328	+	0.0816110i
$417$	−38.4826	+	12.5038i	−1.88450	+	0.612312i
$418$		−	1.46758i		−	0.0717818i
$419$	7.15560	+	22.0227i	0.349574	+	1.07588i	0.959089	+	0.283103i	$0.0913640\pi$
$419$	7.15560	+	22.0227i	0.349574	+	1.07588i	−0.609516	+	0.792774i	$0.708636\pi$
$420$	8.67323	+	4.23684i	0.423210	+	0.206737i
$421$	−10.1155	+	31.1322i	−0.492998	+	1.51729i	0.327056	+	0.945005i	$0.393943\pi$
$421$	−10.1155	+	31.1322i	−0.492998	+	1.51729i	−0.820054	+	0.572286i	$0.806057\pi$
$422$	−16.0932	−	5.22899i	−0.783404	−	0.254543i
$423$	0.744102	+	1.02417i	0.0361795	+	0.0497968i
$424$	−7.50750			−0.364597
$425$	26.4204	−	20.5895i	1.28158	−	0.998737i
$426$	8.20318			0.397446
$427$	−1.15371	−	1.58795i	−0.0558320	−	0.0768462i
$428$	6.54808	+	2.12760i	0.316513	+	0.102841i
$429$	−2.30517	+	7.09458i	−0.111295	+	0.342529i
$430$	5.02036	−	5.19232i	0.242103	−	0.250396i
$431$	−3.72988	−	11.4794i	−0.179662	−	0.552942i	0.820154	−	0.572143i	$-0.193888\pi$
$431$	−3.72988	−	11.4794i	−0.179662	−	0.552942i	−0.999816	+	0.0192007i	$0.993888\pi$
$432$		−	4.98682i		−	0.239928i
$433$	−17.9924	+	5.84608i	−0.864658	+	0.280944i	−0.707573	−	0.706641i	$-0.750210\pi$
$433$	−17.9924	+	5.84608i	−0.864658	+	0.280944i	−0.157085	+	0.987585i	$0.550210\pi$
$434$	−0.419847	−	0.305037i	−0.0201533	−	0.0146422i
$435$	6.09008	−	12.4670i	0.291997	−	0.597747i
$436$	6.16922	−	4.48220i	0.295452	−	0.214658i
$437$	−2.51443	+	3.46082i	−0.120282	+	0.165554i
$438$	15.6236	−	21.5041i	0.746526	−	1.02751i
$439$	−16.4589	+	11.9581i	−0.785539	+	0.570728i	−0.906636	−	0.421913i	$-0.861359\pi$
$439$	−16.4589	+	11.9581i	−0.785539	+	0.570728i	0.121097	+	0.992641i	$0.461359\pi$
$440$	−1.44038	+	2.94861i	−0.0686676	+	0.140569i
$441$	0.218025	+	0.158404i	0.0103821	+	0.00754306i
$442$	−18.0428	+	5.86245i	−0.858206	+	0.278848i
$443$		−	13.0895i		−	0.621903i	−0.950426	−	0.310952i	$-0.899352\pi$
$443$		−	13.0895i		−	0.621903i	0.950426	−	0.310952i	$-0.100648\pi$
$444$	0.299706	+	0.922399i	0.0142234	+	0.0437751i
$445$	−28.4788	+	29.4543i	−1.35003	+	1.39627i
$446$	1.57252	−	4.83973i	0.0744612	−	0.229168i
$447$	12.7631	+	4.14698i	0.603673	+	0.196145i
$448$	−1.41366	−	1.94573i	−0.0667890	−	0.0919272i
$449$	17.3849			0.820444			0.410222	−	0.911986i	$-0.365451\pi$
$449$	17.3849			0.820444			0.410222	+	0.911986i	$0.365451\pi$
$450$	0.377807	+	1.04201i	0.0178100	+	0.0491209i
$451$	−5.70636			−0.268702
$452$	−2.01595	−	2.77472i	−0.0948224	−	0.130512i
$453$	0.694687	+	0.225718i	0.0326393	+	0.0106051i
$454$	−4.91501	+	15.1268i	−0.230673	+	0.709938i
$455$	−13.6841	−	6.68463i	−0.641521	−	0.313380i
$456$	0.554656	+	1.70705i	0.0259741	+	0.0799401i
$457$		−	17.2655i		−	0.807644i	−0.914838	−	0.403822i	$-0.867681\pi$
$457$		−	17.2655i		−	0.807644i	0.914838	−	0.403822i	$-0.132319\pi$
$458$	−12.0831	+	3.92604i	−0.564607	+	0.183452i
$459$	27.0272	+	19.6364i	1.26152	+	0.916549i
$460$	8.44858	−	4.48551i	0.393917	−	0.209138i
$461$	7.21161	−	5.23954i	0.335878	−	0.244030i	−0.407043	−	0.913409i	$-0.633440\pi$
$461$	7.21161	−	5.23954i	0.335878	−	0.244030i	0.742921	+	0.669379i	$0.233440\pi$
$462$	3.72381	−	5.12539i	0.173247	−	0.238455i
$463$	−24.0792	+	33.1422i	−1.11906	+	1.54025i	−0.311702	+	0.950180i	$0.600899\pi$
$463$	−24.0792	+	33.1422i	−1.11906	+	1.54025i	−0.807354	+	0.590068i	$0.799101\pi$
$464$	−2.79682	+	2.03201i	−0.129839	+	0.0943335i
$465$	−0.149859	−	0.852968i	−0.00694955	−	0.0395555i
$466$	2.88541	+	2.09638i	0.133664	+	0.0971127i
$467$	−13.2803	+	4.31502i	−0.614538	+	0.199675i	−0.599714	−	0.800215i	$-0.704719\pi$
$467$	−13.2803	+	4.31502i	−0.614538	+	0.199675i	−0.0148241	+	0.999890i	$0.504719\pi$
$468$		−	0.627768i		−	0.0290186i
$469$	3.22947	+	9.93930i	0.149123	+	0.458954i
$470$	−5.98800	−	11.2786i	−0.276206	−	0.520241i
$471$	2.21613	−	6.82055i	0.102114	−	0.314274i
$472$	8.71382	+	2.83129i	0.401086	+	0.130321i
$473$	−2.78627	−	3.83497i	−0.128113	−	0.176332i
$474$	6.96174			0.319763
$475$	3.07345	+	3.94385i	0.141019	+	0.180956i
$476$	16.1118			0.738485
$477$	0.978220	+	1.34640i	0.0447896	+	0.0616476i
$478$	−14.7580	−	4.79516i	−0.675015	−	0.219326i
$479$	−11.6240	+	35.7749i	−0.531113	+	1.63460i	0.220787	+	0.975322i	$0.429137\pi$
$479$	−11.6240	+	35.7749i	−0.531113	+	1.63460i	−0.751901	+	0.659277i	$0.770863\pi$
$480$	0.561025	−	3.97412i	0.0256072	−	0.181393i
$481$	−0.472858	−	1.45531i	−0.0215605	−	0.0663563i
$482$		−	7.70950i		−	0.351158i
$483$	−17.5628	+	5.70651i	−0.799136	+	0.259655i
$484$	−7.15673	−	5.19967i	−0.325306	−	0.236348i
$485$	−1.93949	−	0.273796i	−0.0880675	−	0.0124324i
$486$	−1.86004	+	1.35140i	−0.0843732	+	0.0613007i
$487$	−13.4323	+	18.4880i	−0.608675	+	0.837769i	−0.996468	−	0.0839773i	$-0.973238\pi$
$487$	−13.4323	+	18.4880i	−0.608675	+	0.837769i	0.387793	+	0.921747i	$0.373238\pi$
$488$	−0.479703	+	0.660254i	−0.0217151	+	0.0298883i
$489$	31.1360	−	22.6217i	1.40802	−	1.02299i
$490$	−1.95428	−	1.88955i	−0.0882853	−	0.0853614i
$491$	−23.4401	−	17.0302i	−1.05784	−	0.768563i	−0.0841499	−	0.996453i	$-0.526817\pi$
$491$	−23.4401	−	17.0302i	−1.05784	−	0.768563i	−0.973687	+	0.227890i	$0.926817\pi$
$492$	6.63749	−	2.15665i	0.299241	−	0.0972294i
$493$		−	23.1593i		−	1.04304i
$494$	−0.875103	−	2.69329i	−0.0393727	−	0.121177i
$495$	0.716487	−	0.125881i	0.0322037	−	0.00565791i
$496$	−0.0666792	+	0.205218i	−0.00299399	+	0.00921454i
$497$	10.4538	+	3.39664i	0.468916	+	0.152360i
$498$	−6.33206	−	8.71533i	−0.283746	−	0.390543i
$499$	3.25061			0.145517			0.0727587	−	0.997350i	$-0.476820\pi$
$499$	3.25061			0.145517			0.0727587	+	0.997350i	$0.476820\pi$
$500$	−2.30429	−	10.9403i	−0.103051	−	0.489265i
$501$	−5.20574			−0.232575
$502$	3.80024	+	5.23058i	0.169613	+	0.233452i
$503$	23.1296	+	7.51527i	1.03130	+	0.335089i	0.775304	−	0.631589i	$-0.217597\pi$
$503$	23.1296	+	7.51527i	1.03130	+	0.335089i	0.255995	+	0.966678i	$0.417597\pi$
$504$	−0.164752	+	0.507054i	−0.00733863	+	0.0225860i
$505$	−8.40770	+	1.47716i	−0.374138	+	0.0657328i
$506$	−1.94002	−	5.97077i	−0.0862445	−	0.265433i
$507$		−	8.93932i		−	0.397009i
$508$	−0.511975	+	0.166351i	−0.0227152	+	0.00738062i
$509$	−19.8163	−	14.3974i	−0.878340	−	0.638152i	0.0544716	−	0.998515i	$-0.482653\pi$
$509$	−19.8163	−	14.3974i	−0.878340	−	0.638152i	−0.932812	+	0.360364i	$0.882653\pi$
$510$	19.3295	+	18.6894i	0.855926	+	0.827578i
$511$	28.8141	−	20.9347i	1.27466	−	0.926096i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−2.93118	+	4.03442i	−0.129415	+	0.178124i
$514$	−1.85508	+	1.34779i	−0.0818239	+	0.0594485i
$515$	0.501318	+	0.0707708i	0.0220907	+	0.00311853i
$516$	4.69029	+	3.40770i	0.206479	+	0.150016i
$517$	−7.97077	+	2.58986i	−0.350554	+	0.113902i
$518$			1.29956i			0.0570995i
$519$	−6.38469	−	19.6501i	−0.280257	−	0.862542i
$520$	−0.885152	+	6.27013i	−0.0388165	+	0.274964i
$521$	−9.00848	+	27.7253i	−0.394669	+	1.21467i	0.534550	+	0.845137i	$0.320481\pi$
$521$	−9.00848	+	27.7253i	−0.394669	+	1.21467i	−0.929219	+	0.369529i	$0.879519\pi$
$522$	0.728845	+	0.236816i	0.0319007	+	0.0103652i
$523$	−0.352161	−	0.484709i	−0.0153989	−	0.0211948i	0.801248	−	0.598332i	$-0.204170\pi$
$523$	−0.352161	−	0.484709i	−0.0153989	−	0.0211948i	−0.816647	+	0.577137i	$0.804170\pi$
$524$	12.6025			0.550543
$525$	0.726683	+	21.5720i	0.0317150	+	0.941479i
$526$	−25.4595			−1.11009
$527$	−0.849663	−	1.16946i	−0.0370119	−	0.0509425i
$528$	−2.50524	−	0.814003i	−0.109027	−	0.0354249i
$529$	1.45248	−	4.47027i	0.0631513	−	0.194360i
$530$	−7.87201	−	14.8271i	−0.341938	−	0.644050i
$531$	−0.627635	−	1.93166i	−0.0272370	−	0.0838270i
$532$			2.40506i			0.104272i
$533$	−10.4722	+	3.40264i	−0.453603	+	0.147385i
$534$	−26.6065	−	19.3307i	−1.15138	−	0.836523i
$535$	2.66404	+	15.1632i	0.115177	+	0.655562i
$536$	3.51546	−	2.55413i	0.151845	−	0.110322i
$537$	−8.65667	+	11.9149i	−0.373563	+	0.514165i
$538$	−15.8071	+	21.7566i	−0.681491	+	0.937992i
$539$	−1.44340	+	1.04869i	−0.0621716	+	0.0451703i
$540$	9.84886	−	5.22894i	0.423827	−	0.225018i
$541$	−5.10928	−	3.71211i	−0.219665	−	0.159596i	0.472511	−	0.881325i	$-0.343348\pi$
$541$	−5.10928	−	3.71211i	−0.219665	−	0.159596i	−0.692176	+	0.721729i	$0.743348\pi$
$542$	26.2066	−	8.51503i	1.12567	−	0.365752i
$543$			2.33187i			0.100070i
$544$	−2.07015	−	6.37127i	−0.0887570	−	0.273166i
$545$	15.3210	+	7.48424i	0.656279	+	0.320590i
$546$	3.77768	−	11.6265i	0.161670	−	0.497569i
$547$	27.0647	+	8.79385i	1.15720	+	0.375998i	0.823852	−	0.566805i	$-0.191821\pi$
$547$	27.0647	+	8.79385i	1.15720	+	0.375998i	0.333350	+	0.942803i	$0.391821\pi$
$548$	12.3145	+	16.9494i	0.526049	+	0.724044i
$549$	0.180915			0.00772128
$550$	−7.33375	+	0.247048i	−0.312712	+	0.0105342i
$551$	3.45706			0.147276
$552$	4.51317	+	6.21184i	0.192093	+	0.264394i
$553$	8.87174	+	2.88260i	0.377265	+	0.122581i
$554$	−8.54370	+	26.2948i	−0.362987	+	1.11716i
$555$	−1.50746	+	1.55910i	−0.0639881	+	0.0661800i
$556$	6.96626	+	21.4399i	0.295435	+	0.909256i
$557$			13.7026i			0.580600i	0.956936	+	0.290300i	$0.0937551\pi$
$557$			13.7026i			0.580600i	−0.956936	+	0.290300i	$0.906245\pi$
$558$	0.0454922	−	0.0147813i	0.00192584	−	0.000625743i
$559$	−7.40007	−	5.37646i	−0.312990	−	0.227400i
$560$	2.36048	−	4.83214i	0.0997486	−	0.204195i
$561$	14.2765	−	10.3725i	0.602753	−	0.437926i
$562$	−16.9299	+	23.3019i	−0.714143	+	0.982933i
$563$	22.7950	−	31.3746i	0.960693	−	1.32228i	0.0140832	−	0.999901i	$-0.495517\pi$
$563$	22.7950	−	31.3746i	0.960693	−	1.32228i	0.946610	−	0.322380i	$-0.104483\pi$
$564$	8.29259	−	6.02492i	0.349181	−	0.253695i
$565$	3.36618	−	6.89090i	0.141616	−	0.289902i
$566$	13.6679	+	9.93029i	0.574504	+	0.417401i
$567$	−21.9949	+	7.14657i	−0.923698	+	0.300128i
$568$		−	4.57026i		−	0.191764i
$569$	−8.84283	−	27.2154i	−0.370711	−	1.14093i	−0.946327	−	0.323211i	$-0.895238\pi$
$569$	−8.84283	−	27.2154i	−0.370711	−	1.14093i	0.575616	−	0.817720i	$-0.304762\pi$
$570$	−2.78981	+	2.88537i	−0.116852	+	0.120855i
$571$	0.685617	−	2.11011i	0.0286922	−	0.0883054i	−0.935685	−	0.352837i	$-0.885217\pi$
$571$	0.685617	−	2.11011i	0.0286922	−	0.0883054i	0.964377	+	0.264531i	$0.0852172\pi$
$572$	3.95262	+	1.28429i	0.165268	+	0.0536987i
$573$	9.87372	+	13.5900i	0.412481	+	0.567731i
$574$	9.35152			0.390325
$575$	17.7176	+	11.9825i	0.738874	+	0.499703i
$576$	0.221678			0.00923658
$577$	−25.6380	−	35.2876i	−1.06732	−	1.46904i	−0.872758	−	0.488153i	$-0.837671\pi$
$577$	−25.6380	−	35.2876i	−1.06732	−	1.46904i	−0.194564	−	0.980890i	$-0.562329\pi$
$578$	26.5142	+	8.61497i	1.10284	+	0.358336i
$579$	0.973606	−	2.99645i	0.0404617	−	0.124528i
$580$	−6.94578	−	3.39298i	−0.288408	−	0.140886i
$581$	−4.46060	−	13.7283i	−0.185057	−	0.569546i
$582$		−	1.57227i		−	0.0651728i
$583$	−10.4786	+	3.40471i	−0.433980	+	0.141009i
$584$	−11.9806	−	8.70445i	−0.495762	−	0.360193i
$585$	1.23983	−	0.658248i	0.0512605	−	0.0272152i
$586$	21.2883	−	15.4668i	0.879410	−	0.638929i
$587$	26.3184	−	36.2242i	1.08628	−	1.49513i	0.233858	−	0.972271i	$-0.424865\pi$
$587$	26.3184	−	36.2242i	1.08628	−	1.49513i	0.852418	−	0.522861i	$-0.175135\pi$
$588$	1.28258	−	1.76533i	0.0528929	−	0.0728008i
$589$	0.174568	−	0.126831i	0.00719297	−	0.00522600i
$590$	3.54517	+	20.1784i	0.145952	+	0.830730i
$591$	−8.18404	−	5.94606i	−0.336647	−	0.244588i
$592$	0.513899	−	0.166976i	0.0211211	−	0.00686267i
$593$		−	17.0621i		−	0.700655i	−0.936627	−	0.350327i	$-0.886070\pi$
$593$		−	17.0621i		−	0.700655i	0.936627	−	0.350327i	$-0.113930\pi$
$594$	−2.26156	−	6.96037i	−0.0927930	−	0.285588i
$595$	16.8941	+	31.8205i	0.692592	+	1.30451i
$596$	2.31042	−	7.11074i	0.0946385	−	0.291267i
$597$	−9.15765	−	2.97550i	−0.374798	−	0.121779i
$598$	−7.12061	−	9.80068i	−0.291183	−	0.400779i
$599$	−13.6425			−0.557417			−0.278709	−	0.960376i	$-0.589906\pi$
$599$	−13.6425			−0.557417			−0.278709	+	0.960376i	$0.589906\pi$
$600$	8.43706	−	3.05907i	0.344442	−	0.124886i
$601$	9.69749			0.395569			0.197784	−	0.980246i	$-0.436625\pi$
$601$	9.69749			0.395569			0.197784	+	0.980246i	$0.436625\pi$
$602$	4.56610	+	6.28470i	0.186100	+	0.256145i
$603$	−0.916121	−	0.297666i	−0.0373073	−	0.0121219i
$604$	0.125755	−	0.387033i	0.00511689	−	0.0157482i
$605$	2.76502	−	19.5865i	0.112414	−	0.796305i
$606$	−2.11747	−	6.51690i	−0.0860163	−	0.264731i
$607$			14.3152i			0.581038i	0.956869	+	0.290519i	$0.0938279\pi$
$607$			14.3152i			0.581038i	−0.956869	+	0.290519i	$0.906172\pi$
$608$	0.951057	−	0.309017i	0.0385704	−	0.0125323i
$609$	12.0734	+	8.77186i	0.489240	+	0.355454i
$610$	−1.80698	−	0.255091i	−0.0731625	−	0.0103283i
$611$	−13.0836	+	9.50576i	−0.529304	+	0.384562i
$612$	−0.872892	+	1.20143i	−0.0352846	+	0.0485651i
$613$	13.9620	−	19.2170i	0.563919	−	0.776168i	−0.427899	−	0.903827i	$-0.640746\pi$
$613$	13.9620	−	19.2170i	0.563919	−	0.776168i	0.991818	+	0.127658i	$0.0407461\pi$
$614$	−20.5971	+	14.9647i	−0.831232	+	0.603925i
$615$	11.2191	+	10.8475i	0.452398	+	0.437415i
$616$	−2.85552	−	2.07466i	−0.115052	−	0.0835904i
$617$	18.2284	−	5.92277i	0.733848	−	0.238442i	0.0818315	−	0.996646i	$-0.473923\pi$
$617$	18.2284	−	5.92277i	0.733848	−	0.238442i	0.652017	+	0.758204i	$0.273923\pi$
$618$			0.406400i			0.0163478i
$619$	3.05126	+	9.39080i	0.122640	+	0.377448i	0.993464	−	0.114148i	$-0.0364137\pi$
$619$	3.05126	+	9.39080i	0.122640	+	0.377448i	−0.870823	+	0.491596i	$0.836414\pi$
$620$	−0.475217	+	0.0834915i	−0.0190852	+	0.00335310i
$621$	−6.59216	+	20.2886i	−0.264534	+	0.814153i
$622$	14.3865	+	4.67444i	0.576844	+	0.187428i
$623$	−25.9020	−	35.6510i	−1.03774	−	1.42833i
$624$	−5.08297			−0.203482
$625$	19.1907	−	16.0224i	0.767627	−	0.640897i
$626$	8.88615			0.355162
$627$	1.54833	+	2.13109i	0.0618342	+	0.0851074i
$628$	−3.79995	−	1.23468i	−0.151635	−	0.0492691i
$629$	−1.11860	+	3.44269i	−0.0446014	+	0.137269i
$630$	−1.17417	+	0.206292i	−0.0467801	+	0.00821886i
$631$	−9.27951	−	28.5594i	−0.369411	−	1.13693i	−0.947172	−	0.320725i	$-0.896073\pi$
$631$	−9.27951	−	28.5594i	−0.369411	−	1.13693i	0.577761	−	0.816206i	$-0.303927\pi$
$632$		−	3.87862i		−	0.154283i
$633$	28.8857	−	9.38554i	1.14810	−	0.373042i
$634$	27.7970	+	20.1957i	1.10396	+	0.802073i
$635$	−0.865372	−	0.836711i	−0.0343412	−	0.0332039i
$636$	10.9017	−	7.92055i	0.432280	−	0.314070i
$637$	−2.02359	+	2.78523i	−0.0801774	+	0.110355i
$638$	−2.98214	+	4.10456i	−0.118064	+	0.162501i
$639$	−0.819636	+	0.595501i	−0.0324243	+	0.0235576i
$640$	−2.21411	−	0.312565i	−0.0875206	−	0.0123552i
$641$	−0.201988	−	0.146753i	−0.00797803	−	0.00579638i	0.583789	−	0.811905i	$-0.301569\pi$
$641$	−0.201988	−	0.146753i	−0.00797803	−	0.00579638i	−0.591767	+	0.806109i	$0.701569\pi$
$642$	−11.7532	+	3.81883i	−0.463860	+	0.150717i
$643$			40.5420i			1.59882i	0.600786	+	0.799410i	$0.294855\pi$
$643$			40.5420i			1.59882i	−0.600786	+	0.799410i	$0.705145\pi$
$644$	3.17929	+	9.78483i	0.125281	+	0.385576i
$645$	−1.81211	+	12.8364i	−0.0713516	+	0.505432i
$646$	−2.07015	+	6.37127i	−0.0814490	+	0.250674i
$647$	11.4155	+	3.70912i	0.448790	+	0.145821i	0.524687	−	0.851295i	$-0.324182\pi$
$647$	11.4155	+	3.70912i	0.448790	+	0.145821i	−0.0758976	+	0.997116i	$0.524182\pi$
$648$	5.65208	+	7.77942i	0.222035	+	0.305604i
$649$	13.4464			0.527816
$650$	−13.3115	+	4.82641i	−0.522120	+	0.189307i
$651$	0.931482			0.0365077
$652$	−12.6033	−	17.3469i	−0.493582	−	0.679358i
$653$	−5.32407	−	1.72989i	−0.208347	−	0.0676960i	0.202984	−	0.979182i	$-0.434936\pi$
$653$	−5.32407	−	1.72989i	−0.208347	−	0.0676960i	−0.411331	+	0.911486i	$0.634936\pi$
$654$	−4.22957	+	13.0173i	−0.165389	+	0.509015i
$655$	13.2144	+	24.8897i	0.516329	+	0.972519i
$656$	−1.20154	−	3.69797i	−0.0469123	−	0.144381i
$657$			3.28280i			0.128074i
$658$	13.0624	−	4.24423i	0.509226	−	0.165457i
$659$	14.7022	+	10.6818i	0.572716	+	0.416102i	0.836091	−	0.548591i	$-0.184836\pi$
$659$	14.7022	+	10.6818i	0.572716	+	0.416102i	−0.263375	+	0.964694i	$0.584836\pi$
$660$	−1.01924	−	5.80133i	−0.0396740	−	0.225816i
$661$	−37.1283	+	26.9753i	−1.44412	+	1.04922i	−0.456965	+	0.889485i	$0.651063\pi$
$661$	−37.1283	+	26.9753i	−1.44412	+	1.04922i	−0.987160	+	0.159733i	$0.948937\pi$
$662$	16.5346	−	22.7580i	0.642637	−	0.884513i
$663$	20.0150	−	27.5483i	0.777319	−	1.06989i
$664$	−4.85560	+	3.52780i	−0.188434	+	0.136905i
$665$	−4.74993	+	2.52183i	−0.184195	+	0.0977924i
$666$	−0.0969062	−	0.0704064i	−0.00375504	−	0.00272819i
$667$	14.0648	−	4.56994i	0.544592	−	0.176949i
$668$			2.90029i			0.112216i
$669$	2.82253	+	8.68685i	0.109125	+	0.335853i
$670$	8.73049	+	4.26481i	0.337288	+	0.164764i
$671$	−0.370116	+	1.13910i	−0.0142882	+	0.0439745i
$672$	4.10556	+	1.33398i	0.158376	+	0.0514593i
$673$	−15.2393	−	20.9752i	−0.587434	−	0.808533i	0.407052	−	0.913405i	$-0.366557\pi$
$673$	−15.2393	−	20.9752i	−0.587434	−	0.808533i	−0.994486	+	0.104872i	$0.966557\pi$
$674$	4.39635			0.169341
$675$	20.6541	+	13.9684i	0.794977	+	0.537646i
$676$	−4.98039			−0.191553
$677$	−12.1820	−	16.7671i	−0.468193	−	0.644413i	0.507989	−	0.861363i	$-0.330389\pi$
$677$	−12.1820	−	16.7671i	−0.468193	−	0.644413i	−0.976183	+	0.216951i	$0.930389\pi$
$678$	5.85476	+	1.90233i	0.224851	+	0.0730584i
$679$	0.651020	−	2.00363i	0.0249839	−	0.0768924i
$680$	10.4125	−	10.7691i	0.399299	−	0.412977i
$681$	−8.82196	−	27.1512i	−0.338058	−	1.04044i
$682$			0.316673i			0.0121260i
$683$	−1.16375	+	0.378124i	−0.0445295	+	0.0144685i	−0.331197	−	0.943562i	$-0.607452\pi$
$683$	−1.16375	+	0.378124i	−0.0445295	+	0.0144685i	0.286668	+	0.958030i	$0.407452\pi$
$684$	−0.179341	−	0.130299i	−0.00685728	−	0.00498211i
$685$	−20.5624	+	42.0932i	−0.785648	+	1.60830i
$686$	15.9856	−	11.6142i	0.610331	−	0.443432i
$687$	13.4039	−	18.4489i	0.511392	−	0.703871i
$688$	1.89854	−	2.61312i	0.0723812	−	0.0996242i
$689$	−17.2001	+	12.4966i	−0.655270	+	0.476081i
$690$	−7.53595	+	15.4269i	−0.286889	+	0.587290i
$691$	6.93665	+	5.03977i	0.263883	+	0.191722i	0.711857	−	0.702324i	$-0.247854\pi$
$691$	6.93665	+	5.03977i	0.263883	+	0.191722i	−0.447974	+	0.894046i	$0.647854\pi$
$692$	−10.9477	+	3.55712i	−0.416169	+	0.135221i
$693$			0.782439i			0.0297224i
$694$	1.22909	+	3.78274i	0.0466555	+	0.143591i
$695$	−35.0389	+	36.2391i	−1.32910	+	1.37463i
$696$	1.91748	−	5.90138i	0.0726817	−	0.223691i
$697$	24.7732	+	8.04931i	0.938353	+	0.304889i
$698$	5.28152	+	7.26938i	0.199908	+	0.275150i
$699$	−6.40164			−0.242132
$700$	12.0185	−	0.404859i	0.454255	−	0.0153022i
$701$	19.4082			0.733038			0.366519	−	0.930410i	$-0.380549\pi$
$701$	19.4082			0.733038			0.366519	+	0.930410i	$0.380549\pi$
$702$	−8.30078	−	11.4250i	−0.313293	−	0.431211i
$703$	−0.513899	−	0.166976i	−0.0193821	−	0.00629762i
$704$	−0.453508	+	1.39575i	−0.0170922	+	0.0526045i
$705$	20.5943	+	10.0602i	0.775626	+	0.378890i
$706$	6.20114	+	19.0851i	0.233383	+	0.718279i
$707$		−	9.18161i		−	0.345310i
$708$	−15.6405	+	5.08190i	−0.587805	+	0.190989i
$709$	−23.0547	−	16.7502i	−0.865836	−	0.629067i	0.0636305	−	0.997974i	$-0.479732\pi$
$709$	−23.0547	−	16.7502i	−0.865836	−	0.629067i	−0.929466	+	0.368907i	$0.879732\pi$
$710$	9.02617	−	4.79217i	0.338746	−	0.179847i
$711$	−0.695595	+	0.505380i	−0.0260869	+	0.0189532i
$712$	−10.7698	+	14.8234i	−0.403615	+	0.555529i
$713$	0.542561	−	0.746771i	0.0203191	−	0.0279668i
$714$	−23.3961	+	16.9983i	−0.875578	+	0.636145i
$715$	1.60810	+	9.15299i	0.0601396	+	0.342302i
$716$	6.63818	+	4.82292i	0.248080	+	0.180241i
$717$	26.4892	−	8.60686i	0.989257	−	0.321429i
$718$		−	6.22497i		−	0.232314i
$719$	−13.7487	−	42.3143i	−0.512741	−	1.57806i	−0.787354	−	0.616501i	$-0.788550\pi$
$719$	−13.7487	−	42.3143i	−0.512741	−	1.57806i	0.274613	−	0.961555i	$-0.411450\pi$
$720$	0.232441	+	0.437809i	0.00866256	+	0.0163162i
$721$	−0.168275	+	0.517898i	−0.00626690	+	0.0192875i
$722$	−0.951057	−	0.309017i	−0.0353947	−	0.0115004i
$723$	8.13365	+	11.1950i	0.302494	+	0.416347i
$724$	1.29916			0.0482829
$725$	−0.581949	−	17.2755i	−0.0216130	−	0.641595i
$726$	15.8781			0.589291
$727$	−18.4590	−	25.4067i	−0.684608	−	0.942282i	0.315370	−	0.948969i	$-0.397871\pi$
$727$	−18.4590	−	25.4067i	−0.684608	−	0.942282i	−0.999978	+	0.00668696i	$0.997871\pi$
$728$	−6.47751	−	2.10467i	−0.240073	−	0.0780043i
$729$	−7.63919	+	23.5110i	−0.282933	+	0.870778i
$730$	4.62875	−	32.7886i	0.171318	−	1.21356i
$731$	6.68657	+	20.5792i	0.247312	+	0.761148i
$732$		−	1.46485i		−	0.0541426i
$733$	23.4186	−	7.60918i	0.864987	−	0.281051i	0.157277	−	0.987555i	$-0.449728\pi$
$733$	23.4186	−	7.60918i	0.864987	−	0.281051i	0.707710	+	0.706503i	$0.249728\pi$
$734$	−6.52015	−	4.73717i	−0.240663	−	0.174852i
$735$	4.83134	+	0.682037i	0.178207	+	0.0251573i
$736$	3.46082	−	2.51443i	0.127568	−	0.0926833i
$737$	3.74840	−	5.15922i	0.138074	−	0.190042i
$738$	−0.506638	+	0.697327i	−0.0186496	+	0.0256690i
$739$	9.78194	−	7.10699i	0.359834	−	0.261435i	−0.393149	−	0.919475i	$-0.628614\pi$
$739$	9.78194	−	7.10699i	0.359834	−	0.261435i	0.752983	+	0.658040i	$0.228614\pi$
$740$	0.868624	+	0.839856i	0.0319313	+	0.0308737i
$741$	4.11221	+	2.98770i	0.151066	+	0.109756i
$742$	17.1723	−	5.57960i	0.630413	−	0.204834i
$743$			4.34363i			0.159352i	0.996821	+	0.0796762i	$0.0253886\pi$
$743$			4.34363i			0.159352i	−0.996821	+	0.0796762i	$0.974611\pi$
$744$	−0.119683	−	0.368346i	−0.00438778	−	0.0135042i
$745$	16.4661	−	2.89296i	0.603273	−	0.105990i
$746$	−0.611312	+	1.88143i	−0.0223817	+	0.0688839i
$747$	1.26536	+	0.411140i	0.0462971	+	0.0150428i
$748$	−5.77885	−	7.95390i	−0.211296	−	0.290823i
$749$	−16.5590			−0.605051
$750$	14.8883	+	13.4554i	0.543644	+	0.491323i
$751$	19.0499			0.695140			0.347570	−	0.937654i	$-0.387007\pi$
$751$	19.0499			0.695140			0.347570	+	0.937654i	$0.387007\pi$
$752$	−3.35668	−	4.62008i	−0.122406	−	0.168477i
$753$	−11.0367	−	3.58604i	−0.402200	−	0.130683i
$754$	−3.02528	+	9.31085i	−0.110174	+	0.339081i
$755$	0.896243	−	0.157462i	0.0326176	−	0.00573064i
$756$	3.70622	+	11.4066i	0.134794	+	0.414853i
$757$		−	35.9424i		−	1.30635i	−0.757208	−	0.653174i	$-0.773437\pi$
$757$		−	35.9424i		−	1.30635i	0.757208	−	0.653174i	$-0.226563\pi$
$758$	−35.5366	+	11.5465i	−1.29075	+	0.419390i
$759$	9.11639	+	6.62345i	0.330904	+	0.240416i
$760$	1.60753	+	1.55429i	0.0583114	+	0.0563802i
$761$	−12.1259	+	8.81000i	−0.439564	+	0.319362i	−0.785462	−	0.618910i	$-0.787575\pi$
$761$	−12.1259	+	8.81000i	−0.439564	+	0.319362i	0.345897	+	0.938272i	$0.387575\pi$
$762$	0.567939	−	0.781702i	0.0205743	−	0.0283181i
$763$	−10.7799	+	14.8373i	−0.390260	+	0.537147i
$764$	7.57145	−	5.50098i	0.273925	−	0.199018i
$765$	−3.28808	−	0.464176i	−0.118881	−	0.0167823i
$766$	−8.80576	−	6.39776i	−0.318165	−	0.231160i
$767$	24.6766	−	8.01792i	0.891021	−	0.289510i
$768$		−	1.79490i		−	0.0647680i
$769$	−1.05589	−	3.24969i	−0.0380762	−	0.117187i	0.930212	−	0.367023i	$-0.119623\pi$
$769$	−1.05589	−	3.24969i	−0.0380762	−	0.117187i	−0.968288	+	0.249837i	$0.919623\pi$
$770$	1.10324	−	7.81498i	0.0397579	−	0.281632i
$771$	1.27183	−	3.91428i	0.0458037	−	0.140969i
$772$	−1.66942	−	0.542428i	−0.0600838	−	0.0195224i
$773$	16.5685	+	22.8045i	0.595927	+	0.820222i	0.995328	−	0.0965537i	$-0.0307820\pi$
$773$	16.5685	+	22.8045i	0.595927	+	0.820222i	−0.399401	+	0.916776i	$0.630782\pi$
$774$	−0.716018			−0.0257367
$775$	−0.663184	−	0.850997i	−0.0238223	−	0.0305687i
$776$	−0.875965			−0.0314453
$777$	−1.37106	−	1.88710i	−0.0491865	−	0.0676994i
$778$	32.5875	+	10.5883i	1.16832	+	0.379610i
$779$	−1.20154	+	3.69797i	−0.0430497	+	0.132493i
$780$	−5.32977	−	10.0388i	−0.190836	−	0.359445i
$781$	−2.07265	−	6.37897i	−0.0741653	−	0.228257i
$782$			28.6577i			1.02480i
$783$	16.3959	−	5.32736i	0.585943	−	0.190384i
$784$	−0.983521	−	0.714570i	−0.0351258	−	0.0255204i
$785$	−1.54599	−	8.79945i	−0.0551787	−	0.314066i
$786$	−18.3002	+	13.2959i	−0.652746	+	0.474248i
$787$	−6.50110	+	8.94800i	−0.231739	+	0.318962i	−0.909012	−	0.416771i	$-0.863162\pi$
$787$	−6.50110	+	8.94800i	−0.231739	+	0.318962i	0.677273	+	0.735732i	$0.263162\pi$
$788$	−3.31274	+	4.55960i	−0.118012	+	0.162429i
$789$	36.9699	−	26.8602i	1.31616	−	0.956250i
$790$	7.66018	−	4.06693i	0.272537	−	0.144695i
$791$	6.67336	+	4.84848i	0.237277	+	0.172392i
$792$	0.309408	−	0.100533i	0.0109943	−	0.00357227i
$793$			2.31116i			0.0820717i
$794$	7.32863	+	22.5552i	0.260083	+	0.800454i
$795$	27.0739	+	13.2255i	0.960213	+	0.469060i
$796$	−1.65775	+	5.10203i	−0.0587574	+	0.180837i
$797$	9.43054	+	3.06417i	0.334047	+	0.108538i	0.471238	−	0.882006i	$-0.343807\pi$
$797$	9.43054	+	3.06417i	0.334047	+	0.108538i	−0.137191	+	0.990545i	$0.543807\pi$
$798$	−2.53738	−	3.49240i	−0.0898222	−	0.123630i
$799$	38.2570			1.35344
$800$	−1.70431	−	4.70057i	−0.0602563	−	0.166190i
$801$	4.06173			0.143514
$802$	−19.5187	−	26.8652i	−0.689231	−	0.948645i
$803$	−20.6696	−	6.71595i	−0.729413	−	0.237001i
$804$	−2.41017	+	7.41774i	−0.0850001	+	0.261603i
$805$	−15.9912	+	16.5389i	−0.563615	+	0.582921i
$806$	0.188828	+	0.581154i	0.00665120	+	0.0204703i
$807$		−	48.2696i		−	1.69917i
$808$	−3.63078	+	1.17971i	−0.127730	+	0.0415021i
$809$	−45.0955	−	32.7638i	−1.58547	−	1.15191i	−0.910064	−	0.414469i	$-0.863967\pi$
$809$	−45.0955	−	32.7638i	−1.58547	−	1.15191i	−0.675408	−	0.737444i	$-0.736033\pi$
$810$	−9.43768	+	19.3199i	−0.331606	+	0.678831i
$811$	−38.6218	+	28.0604i	−1.35620	+	0.985334i	−0.357519	+	0.933906i	$0.616377\pi$
$811$	−38.6218	+	28.0604i	−1.35620	+	0.985334i	−0.998677	+	0.0514285i	$0.983623\pi$
$812$	4.88709	−	6.72651i	0.171503	−	0.236054i
$813$	−29.0712	+	40.0131i	−1.01957	+	1.40332i
$814$	0.641552	−	0.466115i	0.0224864	−	0.0163373i
$815$	21.0446	−	43.0803i	0.737159	−	1.50904i
$816$	9.72789	+	7.06772i	0.340544	+	0.247420i
$817$	−3.07190	+	0.998122i	−0.107472	+	0.0349199i
$818$			19.2365i			0.672589i
$819$	0.466559	+	1.43592i	0.0163029	+	0.0501752i
$820$	6.04352	−	6.25053i	0.211049	−	0.218278i
$821$	−3.88562	+	11.9587i	−0.135609	+	0.417362i	−0.995684	−	0.0928053i	$-0.970417\pi$
$821$	−3.88562	+	11.9587i	−0.135609	+	0.417362i	0.860075	+	0.510167i	$0.170417\pi$
$822$	−35.7639	−	11.6204i	−1.24741	−	0.405308i
$823$	−8.78124	−	12.0863i	−0.306095	−	0.421303i	0.628064	−	0.778162i	$-0.283848\pi$
$823$	−8.78124	−	12.0863i	−0.306095	−	0.421303i	−0.934158	+	0.356859i	$0.883848\pi$
$824$	0.226419			0.00788768
$825$	10.3888	−	8.09598i	0.361690	−	0.281866i
$826$	−22.0358			−0.766722
$827$	−17.5333	−	24.1325i	−0.609693	−	0.839171i	0.386859	−	0.922139i	$-0.373560\pi$
$827$	−17.5333	−	24.1325i	−0.609693	−	0.839171i	−0.996552	+	0.0829680i	$0.973560\pi$
$828$	−0.901883	−	0.293040i	−0.0313426	−	0.0101838i
$829$	9.36939	−	28.8360i	0.325413	−	1.00152i	−0.645842	−	0.763471i	$-0.723493\pi$
$829$	9.36939	−	28.8360i	0.325413	−	1.00152i	0.971254	−	0.238045i	$-0.0765067\pi$
$830$	−12.0587	−	5.89062i	−0.418563	−	0.204466i
$831$	−15.3351	−	47.1966i	−0.531969	−	1.63723i
$832$			2.83189i			0.0981782i
$833$	7.74555	−	2.51668i	0.268367	−	0.0871979i
$834$	−32.7353	−	23.7836i	−1.13353	−	0.823558i
$835$	−5.72801	+	3.04111i	−0.198226	+	0.105242i
$836$	1.18730	−	0.862623i	0.0410636	−	0.0298345i
$837$	0.632485	−	0.870542i	0.0218619	−	0.0300903i
$838$	−13.6108	+	18.7336i	−0.470176	+	0.647141i
$839$	15.1622	−	11.0160i	0.523456	−	0.380313i	−0.294448	−	0.955667i	$-0.595136\pi$
$839$	15.1622	−	11.0160i	0.523456	−	0.380313i	0.817904	+	0.575355i	$0.195136\pi$
$840$	1.67032	+	9.50714i	0.0576316	+	0.328028i
$841$	13.7927	+	10.0210i	0.475612	+	0.345552i
$842$	−31.1322	+	10.1155i	−1.07289	+	0.348602i
$843$		−	51.6982i		−	1.78058i
$844$	−5.22899	−	16.0932i	−0.179989	−	0.553950i
$845$	−5.22220	−	9.83616i	−0.179649	−	0.338374i
$846$	−0.391198	+	1.20398i	−0.0134496	+	0.0413938i
$847$	20.2343	+	6.57453i	0.695259	+	0.225903i
$848$	−4.41280	−	6.07370i	−0.151536	−	0.208572i
$849$	−30.3239			−1.04071
$850$	32.1868	+	9.27237i	1.10400	+	0.318040i
$851$	−2.31150			−0.0792371
$852$	4.82171	+	6.63651i	0.165189	+	0.227363i
$853$	−42.3279	−	13.7532i	−1.44928	−	0.470900i	−0.524504	−	0.851408i	$-0.675749\pi$
$853$	−42.3279	−	13.7532i	−1.44928	−	0.470900i	−0.924778	+	0.380508i	$0.875749\pi$
$854$	0.606542	−	1.86675i	0.0207555	−	0.0638787i
$855$	0.0692888	−	0.490820i	0.00236963	−	0.0167857i
$856$	2.12760	+	6.54808i	0.0727198	+	0.223809i
$857$			8.39652i			0.286820i	0.989663	+	0.143410i	$0.0458067\pi$
$857$			8.39652i			0.286820i	−0.989663	+	0.143410i	$0.954193\pi$
$858$	−7.09458	+	2.30517i	−0.242205	+	0.0786971i
$859$	20.3157	+	14.7602i	0.693162	+	0.503612i	0.877698	−	0.479214i	$-0.159078\pi$
$859$	20.3157	+	14.7602i	0.693162	+	0.503612i	−0.184536	+	0.982826i	$0.559078\pi$
$860$	7.15157	+	1.00958i	0.243867	+	0.0344265i
$861$	−13.5794	+	9.86601i	−0.462785	+	0.336233i
$862$	7.09465	−	9.76495i	0.241645	−	0.332595i
$863$	−14.0456	+	19.3321i	−0.478118	+	0.658073i	−0.978142	−	0.207939i	$-0.933325\pi$
$863$	−14.0456	+	19.3321i	−0.478118	+	0.658073i	0.500024	+	0.866012i	$0.333325\pi$
$864$	4.03442	−	2.93118i	0.137254	−	0.0997207i
$865$	−18.5045	−	17.8916i	−0.629171	−	0.608333i
$866$	−15.3052	−	11.1199i	−0.520093	−	0.377869i
$867$	−47.5903	+	15.4630i	−1.61625	+	0.525152i
$868$		−	0.518960i		−	0.0176146i
$869$	−1.75898	−	5.41359i	−0.0596694	−	0.183644i
$870$	13.6657	−	2.40094i	0.463310	−	0.0813995i
$871$	3.80262	−	11.7033i	0.128847	−	0.396550i
$872$	7.25235	+	2.35643i	0.245596	+	0.0797988i
$873$	0.114137	+	0.157096i	0.00386296	+	0.00531691i
$874$	−4.27781			−0.144699
$875$	13.4016	+	23.3117i	0.453056	+	0.788079i
$876$	26.5805			0.898073
$877$	−30.9336	−	42.5764i	−1.04455	−	1.43770i	−0.893437	−	0.449188i	$-0.851713\pi$
$877$	−30.9336	−	42.5764i	−1.04455	−	1.43770i	−0.151116	−	0.988516i	$-0.548287\pi$
$878$	−19.3486	−	6.28673i	−0.652983	−	0.212167i
$879$	−14.5951	+	44.9190i	−0.492279	+	1.51508i
$880$	−3.23211	+	0.567854i	−0.108954	+	0.0191424i
$881$	3.26968	+	10.0630i	0.110158	+	0.339032i	0.990906	−	0.134553i	$-0.0429597\pi$
$881$	3.26968	+	10.0630i	0.110158	+	0.339032i	−0.880748	+	0.473585i	$0.842960\pi$
$882$			0.269494i			0.00907432i
$883$	54.0677	−	17.5677i	1.81952	−	0.591199i	0.819694	−	0.572802i	$-0.194144\pi$
$883$	54.0677	−	17.5677i	1.81952	−	0.591199i	0.999831	−	0.0183974i	$-0.00585641\pi$
$884$	−15.3481	−	11.1510i	−0.516212	−	0.375050i
$885$	−26.4365	−	25.5609i	−0.888653	−	0.859222i
$886$	10.5897	−	7.69384i	0.355767	−	0.258480i
$887$	28.5384	−	39.2797i	0.958226	−	1.31888i	0.0104502	−	0.999945i	$-0.496674\pi$
$887$	28.5384	−	39.2797i	0.958226	−	1.31888i	0.947775	−	0.318939i	$-0.103326\pi$
$888$	−0.570074	+	0.784640i	−0.0191304	+	0.0263308i
$889$	1.04743	−	0.761003i	0.0351297	−	0.0255232i
$890$	−40.5685	−	5.72704i	−1.35986	−	0.191971i
$891$	11.4169	+	8.29489i	0.382482	+	0.277889i
$892$	4.83973	−	1.57252i	0.162046	−	0.0526520i
$893$			5.71073i			0.191102i
$894$	4.14698	+	12.7631i	0.138696	+	0.426862i
$895$	−2.56467	+	18.1673i	−0.0857276	+	0.607267i
$896$	0.743204	−	2.28735i	0.0248287	−	0.0764148i
$897$	20.6798	+	6.71927i	0.690477	+	0.224350i
$898$	10.2186	+	14.0647i	0.340998	+	0.469344i
$899$	−0.745958			−0.0248791
$900$	−0.620936	+	0.918131i	−0.0206979	+	0.0306044i
$901$	50.2939			1.67553
$902$	−3.35411	−	4.61654i	−0.111680	−	0.153714i
$903$	−13.2609	−	4.30874i	−0.441296	−	0.143386i
$904$	1.05985	−	3.26188i	0.0352500	−	0.108488i
$905$	1.36224	+	2.56581i	0.0452823	+	0.0852905i
$906$	0.225718	+	0.694687i	0.00749897	+	0.0230794i
$907$		−	1.58723i		−	0.0527030i	−0.999653	−	0.0263515i	$-0.991611\pi$
$907$		−	1.58723i		−	0.0527030i	0.999653	−	0.0263515i	$-0.00838892\pi$
$908$	−15.1268	+	4.91501i	−0.502002	+	0.163110i
$909$	0.684658	+	0.497433i	0.0227087	+	0.0164988i
$910$	−2.63534	−	14.9998i	−0.0873606	−	0.497239i
$911$	4.12689	−	2.99836i	0.136730	−	0.0993402i	−0.517318	−	0.855793i	$-0.673069\pi$
$911$	4.12689	−	2.99836i	0.136730	−	0.0993402i	0.654048	+	0.756453i	$0.273069\pi$
$912$	−1.05502	+	1.45211i	−0.0349351	+	0.0480841i
$913$	−5.17734	+	7.12599i	−0.171345	+	0.235836i
$914$	13.9681	−	10.1484i	0.462022	−	0.335679i
$915$	2.89305	−	1.53598i	0.0956414	−	0.0507778i
$916$	−10.2785	−	7.46777i	−0.339612	−	0.246742i
$917$	−28.8263	+	9.36622i	−0.951927	+	0.309300i
$918$			33.4075i			1.10261i
$919$	4.38610	+	13.4990i	0.144684	+	0.445292i	0.996970	−	0.0777839i	$-0.0247844\pi$
$919$	4.38610	+	13.4990i	0.144684	+	0.445292i	−0.852286	+	0.523076i	$0.824784\pi$
$920$	8.59481	+	4.19853i	0.283362	+	0.138421i
$921$	14.1212	−	43.4607i	0.465310	−	1.43208i
$922$	8.47776	+	2.75459i	0.279200	+	0.0907176i
$923$	−7.60741	−	10.4707i	−0.250401	−	0.344647i
$924$	6.33533			0.208417
$925$	−0.747898	+	2.59615i	−0.0245907	+	0.0853608i
$926$	−40.9660			−1.34623
$927$	−0.0295022	−	0.0406062i	−0.000968978	−	0.00133368i
$928$	−3.28786	−	1.06829i	−0.107929	−	0.0350683i
$929$	3.57816	−	11.0124i	0.117396	−	0.361306i	−0.875044	−	0.484044i	$-0.839167\pi$
$929$	3.57816	−	11.0124i	0.117396	−	0.361306i	0.992439	+	0.122738i	$0.0391674\pi$
$930$	0.601981	−	0.622601i	0.0197397	−	0.0204159i
$931$	0.375672	+	1.15620i	0.0123121	+	0.0378929i
$932$			3.56657i			0.116827i
$933$	−25.8223	+	8.39017i	−0.845384	+	0.274682i
$934$	−11.2969	−	8.20766i	−0.369645	−	0.268563i
$935$	9.64934	−	19.7532i	0.315567	−	0.645998i
$936$	0.507875	−	0.368993i	0.0166004	−	0.0120609i
$937$	20.6383	−	28.4062i	0.674224	−	0.927989i	−0.325623	−	0.945500i	$-0.605574\pi$
$937$	20.6383	−	28.4062i	0.674224	−	0.927989i	0.999847	+	0.0175103i	$0.00557397\pi$
$938$	−6.14283	+	8.45488i	−0.200570	+	0.276061i
$939$	−12.9036	+	9.37505i	−0.421095	+	0.305943i
$940$	5.60489	−	11.4738i	0.182811	−	0.374233i
$941$	−36.4527	−	26.4844i	−1.18832	−	0.863367i	−0.195237	−	0.980756i	$-0.562548\pi$
$941$	−36.4527	−	26.4844i	−1.18832	−	0.863367i	−0.993086	+	0.117389i	$0.962548\pi$
$942$	6.82055	−	2.21613i	0.222226	−	0.0722054i
$943$			16.6333i			0.541655i
$944$	2.83129	+	8.71382i	0.0921507	+	0.283611i
$945$	−18.6416	+	19.2801i	−0.606410	+	0.627182i
$946$	1.46483	−	4.50827i	0.0476256	−	0.146577i
$947$	23.5486	+	7.65139i	0.765225	+	0.248637i	0.665520	−	0.746380i	$-0.268210\pi$
$947$	23.5486	+	7.65139i	0.765225	+	0.248637i	0.0997054	+	0.995017i	$0.468210\pi$
$948$	4.09201	+	5.63217i	0.132902	+	0.182924i
$949$	−41.9372			−1.36134
$950$	−1.38411	+	4.80461i	−0.0449065	+	0.155882i
$951$	−61.6710			−1.99982
$952$	9.47030	+	13.0348i	0.306934	+	0.422459i
$953$	−46.4665	−	15.0979i	−1.50520	−	0.489068i	−0.563668	−	0.826001i	$-0.690610\pi$
$953$	−46.4665	−	15.0979i	−1.50520	−	0.489068i	−0.941529	+	0.336933i	$0.890610\pi$
$954$	−0.514281	+	1.58279i	−0.0166504	+	0.0512448i
$955$	18.8034	+	9.18537i	0.608463	+	0.297232i
$956$	−4.79516	−	14.7580i	−0.155087	−	0.477308i
$957$		−	9.10647i		−	0.294370i
$958$	−35.7749	+	11.6240i	−1.15584	+	0.375554i
$959$	−40.7644	−	29.6170i	−1.31635	−	0.956384i
$960$	3.54489	−	1.88205i	0.114411	−	0.0607429i
$961$	25.0419	−	18.1940i	0.807802	−	0.586902i
$962$	0.899429	−	1.23796i	0.0289988	−	0.0399134i
$963$	0.897115	−	1.23477i	0.0289091	−	0.0397900i
$964$	6.23711	−	4.53153i	0.200884	−	0.145951i
$965$	−0.679194	−	3.86583i	−0.0218640	−	0.124446i
$966$	−14.9398	−	10.8544i	−0.480681	−	0.349235i
$967$	−17.5859	+	5.71400i	−0.565524	+	0.183750i	−0.577805	−	0.816175i	$-0.696091\pi$
$967$	−17.5859	+	5.71400i	−0.565524	+	0.183750i	0.0122812	+	0.999925i	$0.496091\pi$
$968$		−	8.84620i		−	0.284328i
$969$	−3.71572	−	11.4358i	−0.119366	−	0.367371i
$970$	−0.918495	−	1.73001i	−0.0294911	−	0.0555473i
$971$	14.3467	−	44.1545i	0.460406	−	1.41698i	−0.404263	−	0.914643i	$-0.632472\pi$
$971$	14.3467	−	44.1545i	0.460406	−	1.41698i	0.864669	−	0.502342i	$-0.167528\pi$
$972$	−2.18661	−	0.710473i	−0.0701356	−	0.0227884i
$973$	−31.8685	−	43.8632i	−1.02166	−	1.40619i
$974$	−22.8524			−0.732237
$975$	14.2378	−	21.0523i	0.455974	−	0.674214i
$976$	−0.816119			−0.0261233
$977$	−12.7975	−	17.6143i	−0.409430	−	0.563532i	0.553649	−	0.832750i	$-0.313235\pi$
$977$	−12.7975	−	17.6143i	−0.409430	−	0.563532i	−0.963079	+	0.269218i	$0.913235\pi$
$978$	36.6026	+	11.8929i	1.17042	+	0.380293i
$979$	−8.30948	+	25.5739i	−0.265572	+	0.817347i
$980$	0.379986	−	2.69170i	0.0121382	−	0.0859831i
$981$	−0.522369	−	1.60769i	−0.0166779	−	0.0513294i
$982$		−	28.9736i		−	0.924583i
$983$	−40.3624	+	13.1145i	−1.28736	+	0.418289i	−0.871167	−	0.490987i	$-0.836636\pi$
$983$	−40.3624	+	13.1145i	−1.28736	+	0.418289i	−0.416194	+	0.909276i	$0.636636\pi$
$984$	5.64619	+	4.10220i	0.179994	+	0.130773i
$985$	−12.4787	−	1.76161i	−0.397604	−	0.0561296i
$986$	18.7363	−	13.6127i	0.596685	−	0.433517i
$987$	−14.4903	+	19.9442i	−0.461231	+	0.634829i
$988$	1.66454	−	2.29105i	0.0529562	−	0.0728880i
$989$	−11.1784	+	8.12160i	−0.355453	+	0.258252i
$990$	0.522980	+	0.505660i	0.0166214	+	0.0160709i
$991$	29.2874	+	21.2786i	0.930346	+	0.675936i	0.946077	−	0.323941i	$-0.105008\pi$
$991$	29.2874	+	21.2786i	0.930346	+	0.675936i	−0.0157318	+	0.999876i	$0.505008\pi$
$992$	−0.205218	+	0.0666792i	−0.00651566	+	0.00211707i
$993$			50.4913i			1.60229i
$994$	3.39664	+	10.4538i	0.107735	+	0.331574i
$995$	−11.8146	+	2.07573i	−0.374549	+	0.0658051i
$996$	3.32896	−	10.2455i	0.105482	−	0.324641i
$997$	−45.2163	−	14.6917i	−1.43201	−	0.465289i	−0.512616	−	0.858618i	$-0.671323\pi$
$997$	−45.2163	−	14.6917i	−1.43201	−	0.465289i	−0.919398	+	0.393329i	$0.871323\pi$
$998$	1.91066	+	2.62980i	0.0604809	+	0.0832448i
$999$	−2.69461			−0.0852535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.a.39.15	✓	88
25.9	even	10	inner	950.2.n.a.609.15	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.a.39.15	✓	88	1.1	even	1	trivial
950.2.n.a.609.15	yes	88	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.70705 - 0.554656i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.20234 + 0.386932i) q^{5} +(-0.554656 - 1.70705i) q^{6} -2.40506i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.179341 + 0.130299i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.70705 - 0.554656i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.20234 + 0.386932i) q^{5} +(-0.554656 - 1.70705i) q^{6} -2.40506i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.179341 + 0.130299i) q^{9} +(-1.60753 - 1.55429i) q^{10} +(-1.18730 + 0.862623i) q^{11} +(1.05502 - 1.45211i) q^{12} +(-1.66454 + 2.29105i) q^{13} +(1.94573 - 1.41366i) q^{14} +(3.97412 + 0.561025i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(6.37127 - 2.07015i) q^{17} +0.221678i q^{18} +(0.309017 + 0.951057i) q^{19} +(0.312565 - 2.21411i) q^{20} +(-1.33398 + 4.10556i) q^{21} +(-1.39575 - 0.453508i) q^{22} +(2.51443 + 3.46082i) q^{23} +1.79490 q^{24} +(4.70057 - 1.70431i) q^{25} -2.83189 q^{26} +(2.93118 + 4.03442i) q^{27} +(2.28735 + 0.743204i) q^{28} +(1.06829 - 3.28786i) q^{29} +(1.88205 + 3.54489i) q^{30} +(-0.0666792 - 0.205218i) q^{31} -1.00000i q^{32} +(2.50524 - 0.814003i) q^{33} +(5.41973 + 3.93766i) q^{34} +(0.930593 + 5.29674i) q^{35} +(-0.179341 + 0.130299i) q^{36} +(-0.317607 + 0.437149i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(4.11221 - 2.98770i) q^{39} +(1.97498 - 1.04855i) q^{40} +(3.14568 + 2.28547i) q^{41} +(-4.10556 + 1.33398i) q^{42} +3.22999i q^{43} +(-0.453508 - 1.39575i) q^{44} +(-0.445386 - 0.217569i) q^{45} +(-1.32192 + 4.06844i) q^{46} +(5.43123 + 1.76471i) q^{47} +(1.05502 + 1.45211i) q^{48} +1.21570 q^{49} +(4.14174 + 2.80107i) q^{50} -12.0243 q^{51} +(-1.66454 - 2.29105i) q^{52} +(7.14006 + 2.31995i) q^{53} +(-1.54101 + 4.74275i) q^{54} +(2.28106 - 2.35919i) q^{55} +(0.743204 + 2.28735i) q^{56} -1.79490i q^{57} +(3.28786 - 1.06829i) q^{58} +(-7.41242 - 5.38544i) q^{59} +(-1.76164 + 3.60625i) q^{60} +(0.660254 - 0.479703i) q^{61} +(0.126831 - 0.174568i) q^{62} +(0.313376 - 0.431326i) q^{63} +(0.809017 - 0.587785i) q^{64} +(2.77941 - 5.68972i) q^{65} +(2.13109 + 1.54833i) q^{66} +(-4.13267 + 1.34278i) q^{67} +6.69915i q^{68} +(-2.37271 - 7.30246i) q^{69} +(-3.73817 + 3.86621i) q^{70} +(-1.41229 + 4.34658i) q^{71} +(-0.210828 - 0.0685022i) q^{72} +(8.70445 + 11.9806i) q^{73} -0.540345 q^{74} +(-8.96943 + 0.302148i) q^{75} -1.00000 q^{76} +(2.07466 + 2.85552i) q^{77} +(4.83419 + 1.57072i) q^{78} +(-1.19856 + 3.68878i) q^{79} +(2.00916 + 0.981466i) q^{80} +(-2.97147 - 9.14526i) q^{81} +3.88827i q^{82} +(5.70810 - 1.85467i) q^{83} +(-3.49240 - 2.53738i) q^{84} +(-13.2307 + 7.02442i) q^{85} +(-2.61312 + 1.89854i) q^{86} +(-3.64726 + 5.02002i) q^{87} +(0.862623 - 1.18730i) q^{88} +(14.8234 - 10.7698i) q^{89} +(-0.0857741 - 0.488209i) q^{90} +(5.51010 + 4.00332i) q^{91} +(-4.06844 + 1.32192i) q^{92} +0.387302i q^{93} +(1.76471 + 5.43123i) q^{94} +(-1.04855 - 1.97498i) q^{95} +(-0.554656 + 1.70705i) q^{96} +(0.833092 + 0.270688i) q^{97} +(0.714570 + 0.983521i) q^{98} -0.325331 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

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